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Time & Work, Chain Rule

মোট প্রশ্ন১,০৭৬এই পাতা১০০প্রতি পাতা১০০
প্রশ্ন দেখুনঅনুশীলন
ঘনত্ব
উত্তর
উত্তরিতবর্তমানপুনরায় দেখুনঅসম্পূর্ণ

Time & Work, Chain Rule

PrepBank · পাতা ২ / ১১ · ১০১–২০০ / ১,০৭৬

১০১.
If A can do 1/4 of a work in 3 days and B can do 1/9 of the same work in 4 days, how much will A get if both work together and paid Tk 800 in all?
  1. ক
    500 Tk
  2. খ
    550 Tk
  3. গ
    600 Tk
  4. ঘ
    650 Tk
সঠিক উত্তর: গ
600 Tk
উত্তর
সঠিক উত্তর: গ
600 Tk
গ
ব্যাখ্যা
Question: If A can do 1/4 of a work in 3 days and B can do 1/9 of the same work in 4 days, how much will A get if both work together and paid Tk 800 in all?

Solution:
Whole work is done by A in (3 × 4) = 12 days
∴ A's 1 day's work = 1/12 part
Whole work is done by B in (4 × 9) = 36 days
∴ B's 1 day's work = 1/36 part

A's 1 day's work : B's 1 day's work
= A's wages : B's wages
= 1/12 : 1/36
= 3 : 1

∴ A's share = (800 × 3/4) Tk
= 600 Tk
১০২.
A ferry can carry 25 trucks or 40 motorcycles at a time. If there are 15 trucks on the ferry, how many motorcycles can be loaded onto it?
  1. ক
    18 motorcycles
  2. খ
    8 motorcycles
  3. গ
    12 motorcycles
  4. ঘ
    16 motorcycles
সঠিক উত্তর: ঘ
16 motorcycles
উত্তর
সঠিক উত্তর: ঘ
16 motorcycles
ঘ
ব্যাখ্যা
Question: A ferry can carry 25 trucks or 40 motorcycles at a time. If there are 15 trucks on the ferry, how many motorcycles can be loaded onto it?

Solution:
Here,
25 trucks = 40 motorcycles
∴ 1 trucks = 40/25 = 8/5 motorcycles
∴ 15 trucks = = (8 × 15)/5 = 24 motorcycles

∴ Required number of motorcycles = 40 - 24 = 16

So the ferry can carry 16 more motorcycles along with the 15 trucks.
১০৩.
If 5 workers can collect 75 kg wheat in 3 days, how many kilograms of wheat will 8 workers collect in 5 days?
  1. ক
    160 kg
  2. খ
    200 kg
  3. গ
    320 kg
  4. ঘ
    175 kg
সঠিক উত্তর: খ
200 kg
উত্তর
সঠিক উত্তর: খ
200 kg
খ
ব্যাখ্যা

Question: If 5 workers can collect 75 kg wheat in 3 days, how many kilograms of wheat will 8 workers collect in 5 days ?

Solution: 
5 workers 3 days collection = 75 kg
1 worker 1 day collection = (75/15) kg
8 workers 5 days collection = (75 × 40)/15 kg
= 200 kg

∴ 8 workers will collect 200 kg in 5 days.

১০৪.
A work twice as fast as B. If both of them can together finish a piece of work in 12 days, Then B alone can do it in
  1. ক
    36 days
  2. খ
    34 days
  3. গ
    32 days
  4. ঘ
    38 days
সঠিক উত্তর: ক
36 days
উত্তর
সঠিক উত্তর: ক
36 days
ক
ব্যাখ্যা
Question: A work twice as fast as B. If both of them can together finish a piece of work in 12 days, Then B alone can do it in

Solution:
Let us consider work done by B in 1 day = x
So, the work done by A in 1 day = 2x

Now,
The number of days A and B together requires to complete a piece of work = 12 days

Work done by both A and B together in 1 day = 1/12

ATQ,
2x + x = 1/12
⇒ 3x = 1/12
∴ x = 1/36

∴ B can do work in 36 days.
১০৫.
40 workers can complete a work is 15 days. After six days 20 more workers joined them. How many days will they require to complete the remaining work?
  1. ক
    4
  2. খ
    6
  3. গ
    10
  4. ঘ
    15
সঠিক উত্তর: খ
6
উত্তর
সঠিক উত্তর: খ
6
খ
ব্যাখ্যা

Question: 40 workers can complete a work is 15 days. After six days 20 more workers joined them. How many days will they require to complete the remaining work?

Solution: 
15 days for the full work
∴ 6 day for = 6/15 = 2/5 of the work

∴ remaining work is = (1 - 2/5) = 3/5
And total workers = 40 + 20 = 60


∴ 40 men can do 1 work in 15 days
∴ 40 men can do 3/5 work in = (15 × 3/5) = 9 days
∴ 60 men can do 3/5 work in = (9 × 40)/60 days
= 6 days

১০৬.
A and B can make a dam in 3 day's. B alone can make the dam in 6 day's. In how many days A alone can make the dam?
  1. ক
    ক) 1
  2. খ
    খ) 3
  3. গ
    গ) 5
  4. ঘ
    ঘ) 6
সঠিক উত্তর: ঘ
ঘ) 6
উত্তর
সঠিক উত্তর: ঘ
ঘ) 6
ঘ
ব্যাখ্যা
Question: A and B can make a dam in 3 day's. B alone can make the dam in 6 day's. In how many days A alone can make the dam?

Solution:
A's 1 day's work = ( 1/3 - 1/6 ) = 1/6
∴ A alone can make the dam in 6 day's.
১০৭.
A can do a piece of work in 15 days and the ratio of the efficiency of  A and B is 4 : 1. A, B and C together can complete the half of the work in 4 days. If they got the total wages of Tk. 5700, then what is the wage of C?
  1. ক
    Tk.1300
  2. খ
    Tk.1600
  3. গ
    Tk.1900
  4. ঘ
    Tk.2100
সঠিক উত্তর: গ
Tk.1900
উত্তর
সঠিক উত্তর: গ
Tk.1900
গ
ব্যাখ্যা
Question: A can do a piece of work in 15 days and the ratio of the efficiency of  A and B is 4 : 1. A, B and C together can complete the half of the work in 4 days. If they got the total wages of Tk. 5700, then what is the wage of C?

Solution: 
A can do a piece of work in 15 days
the ratio of the efficiency of  A and B is 4 : 1

B alone complete the work = 4 × 15 = 60 days

A, B and C together can complete the work in = (4 × 2) = 8 days

C's work in one day = 1/8 – 1/15 – 1/60
 = 1/24

Ratio of work done by A, B and C = 1/15 : 1/60 : 1/24
= 8 : 2 : 5

C’s wages = 5/15 × 5700 = Tk.1900
১০৮.
Assurance company has a project that wil take 1000 person days to complete. How many days will it take to complete the project if the company has 50 workers?
  1. ক
    ক) 50
  2. খ
    খ) 43
  3. গ
    গ) 32
  4. ঘ
    ঘ) 20
সঠিক উত্তর: ঘ
ঘ) 20
উত্তর
সঠিক উত্তর: ঘ
ঘ) 20
ঘ
ব্যাখ্যা
প্রশ্নানুসারে ১ টি কাজ শেষ করতে ১ জনের লাগবে ১০০০ দিন
তাহলে, ৫০ জনের লাগবে ১০০০/৫০ = ২০ দিন
১০৯.
If 8 workers can complete a task in 24 days, how many days will it take for 12 workers to complete the same task assuming they all work at the same rate? 
  1. ক
    10 days 
  2. খ
    16 days 
  3. গ
    22 days 
  4. ঘ
    8 days 
সঠিক উত্তর: খ
16 days 
উত্তর
সঠিক উত্তর: খ
16 days 
খ
ব্যাখ্যা

Question: If 8 workers can complete a task in 24 days, how many days will it take for 12 workers to complete the same task assuming they all work at the same rate?

Solution:
8 workers can complete work in 24 days
∴ 1 worker can complete work in = 8 × 24 days
∴ 12 workers can complete work in = (8 × 24)/12 days
= 16 days

It will take 12 workers 16 days to complete the same task.

১১০.
Two pipes A and B can fill the cistern in 10 hour and 12 hour respectively, while C can empty it in 20 hour. If all pipes are opened simultaneously, then the cistern will be filled in-
  1. ক
    19/2 hours
  2. খ
    17/2 hours
  3. গ
    15/2 hours
  4. ঘ
    13/2 hours
  5. ঙ
    11/2 hours
সঠিক উত্তর: গ
15/2 hours
উত্তর
সঠিক উত্তর: গ
15/2 hours
গ
ব্যাখ্যা
Question: Two pipes A and B can fill the cistern in 10 hour and 12 hour respectively, while C can empty it in 20 hour. If all pipes are opened simultaneously, then the cistern will be filled in-

Solution:
in one hour,
A can fill = 1/10
B can fill = 1/12
C can reduce = 1/20

So, in one-hour, total fill up = 1/10 + 1/12 - 1/20
= (6 + 5 - 3)/60
= 8/60
= 2/15

∴ 2/15 part fill up in 1 hour
∴ 1 part fill up in 15/2 hour

So, it will take 15/2 hours to fill the tank if all three pipes are opened together.
১১১.
A man and a boy received Tk. 800 as wages for 5 days for the work they did together . The man's efficiency in the work was four times that of the boy. What are the daily wages of the boy?
  1. ক
    Tk. 50
  2. খ
    Tk. 44
  3. গ
    Tk. 32
  4. ঘ
    Tk. 28
  5. ঙ
    None
সঠিক উত্তর: গ
Tk. 32
উত্তর
সঠিক উত্তর: গ
Tk. 32
গ
ব্যাখ্যা
Question: A man and a boy received Tk. 800 as wages for 5 days for the work they did together . The man's efficiency in the work was four times that of the boy. What are the daily wages of the boy?

Solution:
Man's wage = 4 boy's wage
Daily wages for them = 800/5
= 160

(1 man + 1 boy) = (4 + 1) = 5 boys

5 boys wage = 160
∴ 1 boys wage = 160/5 = Tk. 32

the daily wages of the boy = Tk. 32
১১২.
In a particular country, one person is born every 6 seconds while one person dies every 10 seconds. Based on these birth and death rates, the net increase in population is one person after how many seconds?
  1. ক
    20 seconds
  2. খ
    21 seconds
  3. গ
    15 seconds
  4. ঘ
    10 seconds
  5. ঙ
    5 seconds
সঠিক উত্তর: গ
15 seconds
উত্তর
সঠিক উত্তর: গ
15 seconds
গ
ব্যাখ্যা

Question: In a particular country, one person is born every 6 seconds while one person dies every 10 seconds. Based on these birth and death rates, the net increase in population is one person after how many seconds?

Solution:
Let,
x be the number of seconds for the population to increase by one person.

We know,
Population growth = Birth rate - Death rate 

ATQ,
⇒ 1 person/6 seconds - 1 person/10 seconds = 1 person/x seconds
⇒ (5 - 3) person/30 seconds = 1 person/x seconds
⇒ 2 persons/30 seconds = 1 person/x seconds
⇒ 1 person/15 seconds = 1 person/x seconds

∴ x = 15 seconds

১১৩.
If Aman and Bijoy together can complete a piece of work in 15 days and Bijoy alone in 20 days, in how many days can Aman alone complete the work?
  1. ক
    ক) 40 days
  2. খ
    খ) 50 days
  3. গ
    গ) 60 days
  4. ঘ
    ঘ) 65 days
সঠিক উত্তর: গ
গ) 60 days
উত্তর
সঠিক উত্তর: গ
গ) 60 days
গ
ব্যাখ্যা
Question: If Aman and Bijoy together can complete a piece of work in 15 days and Bijoy alone in 20 days, in how many days can Aman alone complete the work?

Solution: 
Aman and Bijoy together can complete a piece of work in 15 days
Aman and Bijoy together can complete in 1 day = 1/15 

Bijoy alone in 20 days
Bijoy alone in one day = 1/20

Aman complete in one day = (1/15) - (1/20)
= (4 - 3)/60
= 1/60

Aman can complete the work in 60 days
১১৪.
Parimal rented a car for Tk. 1800 plus Tk. 10 per mile driven. Maruf rented a car for Tk. 2500 plus Tk. 5 per mile driven. If each drove d miles and each was charged exactly the same amount for the rental, then d equals-
  1. ক
    100
  2. খ
    120
  3. গ
    135
  4. ঘ
    140
  5. ঙ
    150
সঠিক উত্তর: ঘ
140
উত্তর
সঠিক উত্তর: ঘ
140
ঘ
ব্যাখ্যা
Question: Parimal rented a car for Tk. 1800 plus Tk. 10 per mile driven. Maruf rented a car for Tk. 2500 plus Tk. 5 per mile driven. If each drove d miles and each was charged exactly the same amount for the rental, then d equals-

Solution:
For d miles Parimal's cost would be: 1800 + 10d
And Maruf's cost would be: 2500 + 5d

Since we are told that each was charged exactly the same amount then:
1800 + 10d = 2500 + 5d
⇒ 5d = 700
∴ d = 140
১১৫.
If 10 men can do a piece of work in 12 days, the time taken by 12 men to do the same piece of work will be -
  1. ক
    ক) 8 days
  2. খ
    খ) 9 days
  3. গ
    গ) 10 days
  4. ঘ
    ঘ) 12 days
সঠিক উত্তর: গ
গ) 10 days
উত্তর
সঠিক উত্তর: গ
গ) 10 days
গ
ব্যাখ্যা
Question: If 10 men can do a piece of work in 12 days, the time taken by 12 men to do the same piece of work will be - 

Solution: 
from 10 men can do a piece of work in 12 days, we get - 
M1 = 10
D1 = 12

the time taken by 12 men to do the same piece of work will be
M2 =12
D2 =?

we know that,
M1 × D1 = M2 × D2
D2 = (10 × 12)/12
= 10 days
১১৬.
When 128 guests take seat in auditorium, only 4/5 of the seats occupied. What is the total number of seats in the auditorium?
  1. ক
    150
  2. খ
    160
  3. গ
    168
  4. ঘ
    172
সঠিক উত্তর: খ
160
উত্তর
সঠিক উত্তর: খ
160
খ
ব্যাখ্যা
Question: When 128 guests take seat in auditorium, only 4/5 of the seats occupied. What is the total number of seats in the auditorium?

Solution: 
ধরি,
মোট আসন সংখ্যা x টি 

প্রশ্নমতে,
x × (4/5) = 128
⇒ x = 128 × (5/4)
∴ x = 160 

মোট আসন সংখ্যা ১৬০ টি 
১১৭.
If 6 men can build a wall in 8 days, how many days will 12 men take to build the same wall?
  1. ক
    4 days
  2. খ
    6 days
  3. গ
    8 days
  4. ঘ
    10 days
সঠিক উত্তর: ক
4 days
উত্তর
সঠিক উত্তর: ক
4 days
ক
ব্যাখ্যা

Question: If 6 men can build a wall in 8 days, how many days will 12 men take to build the same wall?

Solution:
6 জন লোক একটি দেয়াল 8 দিনে তৈরি করতে পারে।
1 জন লোক সেই দেয়াল তৈরি করতে লাগবে = (8 × 6) দিন
12 জন লোক সেই দেয়াল তৈরি করতে লাগবে = (8 × 6)/12 দিন
= 4 দিন

১১৮.
A can complete 1/5 of a task in 4 days, while B can complete 1/10 of the same task in 5 days. If they work together and receive a total payment of Tk 900, what amount should A receive?
  1. ক
    400 Tk
  2. খ
    643 Tk
  3. গ
    700 Tk
  4. ঘ
    500 Tk
সঠিক উত্তর: খ
643 Tk
উত্তর
সঠিক উত্তর: খ
643 Tk
খ
ব্যাখ্যা

Question: A can complete 1/5 of a task in 4 days, while B can complete 1/10 of the same task in 5 days. If they work together and receive a total payment of Tk 900, what amount should A receive?

Solution:

Whole work is done by A in (5 × 4) = 20 days
∴ A's 1-day work = (1/5) ÷ 4 = 1/20

Whole work is done by B in (5 × 10) = 50 days
∴ B's 1-day work = (1/10) ÷ 5 = 1/50

Ratio of A's and B's 1-day work = 1/20 : 1/50
= 50 : 20 = 5 : 2

∴ A's share of payment = (5/(5+2)) × 900 
= (5/7) × 900
= 643 Tk

১১৯.
The price of 357 apples is Tk. 1517.25. Find the approximate price of 49 dozens of such apples?
  1. ক
    2288 Tk.
  2. খ
    2499 Tk.
  3. গ
    2377 Tk.
  4. ঘ
    2522 Tk.
সঠিক উত্তর: খ
2499 Tk.
উত্তর
সঠিক উত্তর: খ
2499 Tk.
খ
ব্যাখ্যা
Question: The price of 357 apples is Tk. 1517.25. Find the approximate price of 49 dozens of such apples?

Solution:
1 dozen = 12 pcs
49 dozens = 49 × 12 = 588 apples

Now,
357 apples = 1517.25 Tk.
∴ 1 apple = 1517.25/357 Tk.
∴ 588 apples = (1517.25 × 588)/357 Tk.
= 2499 Tk.
১২০.
54 toymakers can prepare 36 toys per day. Ajay wants 416 toys. How many toymakers should he employ to get the job done in 16 days?
  1. ক
    39
  2. খ
    41
  3. গ
    27
  4. ঘ
    43
  5. ঙ
    None
সঠিক উত্তর: ক
39
উত্তর
সঠিক উত্তর: ক
39
ক
ব্যাখ্যা
Question: 54 toymakers can prepare 36 toys per day. Ajay wants 416 toys. How many toymakers should he employ to get the job done in 16 days?

Solution:
Let, the required number of toymakers x

54 toymakers make 36 toys per day
So, 1 toymaker makes 36/54 = 2/3 toys per day
Each toymaker in 16 days makes = 2/3 × 16 = 32/3 toys
So, x toymakers will make = 32x/3 toys

ATQ,
32x/3 = 416
⇒ x = 416 × (3/32)
∴ x = 39
১২১.
In an election a candidate who gets 84% of the votes is elected by a majority of 476 votes. What is the total number of votes polled?
  1. ক
    ক) 672
  2. খ
    খ) 749
  3. গ
    গ) 700
  4. ঘ
    ঘ) 848
সঠিক উত্তর: গ
গ) 700
উত্তর
সঠিক উত্তর: গ
গ) 700
গ
ব্যাখ্যা
মনেকরি,
মোট ভোট দেয় x জন 

জয়ী প্রার্থী ভোট পায় = x এর 84%
                                = x এর84/100
                                = 84x/100
                                = 21x/25

অপর প্রার্থী ভোট পায় = x এর 16%
                                  = 16x/100
                                 = 4x/25

প্রশ্নমতে,
(21x/25) - (4x/25) = 476
(21x  - 4x)/25 = 476
17x/25 = 476
x  = (476 × 25)/17
x  = 700
১২২.
A man and a boy can finish a job working together for 4 days. The man can work as much as two boys can do. Then in how many days can the man do it alone?
  1. ক
    3 days
  2. খ
    4 days
  3. গ
    6 days
  4. ঘ
    8 days
সঠিক উত্তর: গ
6 days
উত্তর
সঠিক উত্তর: গ
6 days
গ
ব্যাখ্যা
Question: A man and a boy can finish a job working together for 4 days. The man can work as much as two boys can do. Then in how many days can the man do it alone?

Solution: 
1 man and 1 boy can do in 1 day 1/4 part
2 man and 2 boy can do in 1 day 2/4 part = 1/2 part

Now 1 man = 2 boys 
(2 + 1) man can do in 1 day is 1/2 part
3 man can do in 1 day is 1/2 part
1 man can do in 1 day is 1/(2 × 3) part = 1/6 part

∴ Man alone can do the work in 6 days.
১২৩.
If machine A polishes x units in 12 minutes and machine B polishes 5x units in 40 minutes, in how many minutes will A and B, working together, polish 50x units?
  1. ক
    ক) 240
  2. খ
    খ) 300
  3. গ
    গ) 350
  4. ঘ
    ঘ) 120
সঠিক উত্তর: ক
ক) 240
উত্তর
সঠিক উত্তর: ক
ক) 240
ক
ব্যাখ্যা
In 1 minute A polishes x/12 unit and B polishes 5x/40 = x/8 minute
A and B together polishes x/12 + x/8 = 5x/24 units in 1 minute
5x/24 unites requires 1 minute
So, 50x units require = (24 × 50x) / 5x = 240 minutes
১২৪.
If 20 men can build a wall 56 meters long in 6 days , what length of a similar wall can be built by 35 men in 3 days?
  1. ক
    46 meters
  2. খ
    47 meters
  3. গ
    48 meters
  4. ঘ
    49 meters
  5. ঙ
    50 meters
সঠিক উত্তর: ঘ
49 meters
উত্তর
সঠিক উত্তর: ঘ
49 meters
ঘ
ব্যাখ্যা
Question: If 20 men can build a wall 56 meters long in 6 days , what length of a similar wall can be built by 35 men in 3 days?

Solution:
Let the required length be x meters

More men, More length built (Direct proportion)
Less days, Less length built (Direct Proportion)

∴ (20 × 6 × x)=(35 × 3 × 56)
∴ x = 49

Hence, the required length is 49 m.
১২৫.
On a certain airline, the price of a ticket is directly proportional to the number of miles to be traveled. If the ticket for a 900-mile trip on this airline costs Tk. 120, which of the following gives the number of money charged for a k-mile trip on this airline?
  1. ক
    (2k)/15
  2. খ
    2/(15k)
  3. গ
    15/(2k)
  4. ঘ
    (15k)/2
  5. ঙ
    (40k)/3
সঠিক উত্তর: ক
(2k)/15
উত্তর
সঠিক উত্তর: ক
(2k)/15
ক
ব্যাখ্যা
Question: On a certain airline, the price of a ticket is directly proportional to the number of miles to be traveled. If the ticket for a 900-mile trip on this airline costs Tk. 120, which of the following gives the number of money charged for a k-mile trip on this airline?

Solution:
900 mile trip cost Tk. 120
∴ 1 mile trip costs Tk. 120/900 = 2/15
∴ k mile trip will cost Tk. (2k)/15
১২৬.
18 men bind 900 books in 10 days. Find how many binders will be required to bind 600 books in 12 days?
  1. ক
    9
  2. খ
    10
  3. গ
    12
  4. ঘ
    15
সঠিক উত্তর: খ
10
উত্তর
সঠিক উত্তর: খ
10
খ
ব্যাখ্যা
Question: 18 men bind 900 books in 10 days. Find how many binders will be required to bind 600 books in 12 days?

Solution: 
To bind 900 books in 10 days binders needed 18 men 
To bind 1 books in 1 days binders needed 180/900 men 
To bind 600 books in 12 days binders needed (180 × 600)/(900 × 12) men
= 10 men
১২৭.
A garrison of 500 men had food for 50 days. After 10 days a reinforcement of 300 men arrived. For how many more days will the remaining food last now?
  1. ক
    20 days
  2. খ
    22 days
  3. গ
    25 days
  4. ঘ
    28 days
সঠিক উত্তর: গ
25 days
উত্তর
সঠিক উত্তর: গ
25 days
গ
ব্যাখ্যা
Question: A garrison of 500 men had food for 50 days. After 10 days a reinforcement of 300 men arrived. For how many more days will the remaining food last now?

Solution:
After 10 days, food having for = 50 - 10 = 40 days
After arriving 300 men, total men = 500 + 300 = 800 men

500 men can eat the food for 40 days
∴ 1 man can eat the food for (40 × 500) days
∴ 800 men can eat the food for (40 × 500)/800 days
= 25 days
১২৮.
Rahim can hammer 20 nails in 6 minutes. Charlie can do the same job in only 5 minutes. How long will it take them to hammer 22 nails if Rahim hammers the first 5 nails, then Charlie hammers for 3 minutes and finally Rahim finished the job?
  1. ক
    ক) 4.6 minutes
  2. খ
    খ) 5.0 minutes
  3. গ
    গ) 5.4 minutes
  4. ঘ
    ঘ) 6.0 minutes
সঠিক উত্তর: ঘ
ঘ) 6.0 minutes
উত্তর
সঠিক উত্তর: ঘ
ঘ) 6.0 minutes
ঘ
ব্যাখ্যা
Question: Rahim can hammer 20 nails in 6 minutes. Charlie can do the same job in only 5 minutes. How long will it take them to hammer 22 nails if Rahim hammers the first 5 nails, then Charlie hammers for 3 minutes and finally Rahim finished the job? 

Solution:
In 5 Charlie minutes can hammer 20 nails
In 3 Charlie minutes can hammer (20 × 3)/5 = 12 nails
Rest nails = 22 - 12 = 10 nails

Rahim can hammer 20 nails in 6 minutes
Rahim can hammer 5 nails in (6 × 5) / 20 = 1.5 minutes

Rest nails = 10 - 5 = 5 nails

So, the rest 5 nails can hammer Rahim in 1.5 minutes

So, total time taken = 3 + 1.5 + 1.5 = 6 minutes
১২৯.
Robin can paint 60 walls in 20 minutes. Tara can paint 8 walls in 16 minutes. Working together, how many walls can they paint in 40 minutes? 
  1. ক
    100 walls
  2. খ
    120 walls
  3. গ
    40 walls
  4. ঘ
    140 walls
  5. ঙ
    None
সঠিক উত্তর: ঘ
140 walls
উত্তর
সঠিক উত্তর: ঘ
140 walls
ঘ
ব্যাখ্যা

Question: Robin can paint 60 walls in 20 minutes. Tara can paint 8 walls in 16 minutes. Working together, how many walls can they paint in 40 minutes?

Solution:
Robin can paint in 1 minute = 60/20 = 3 walls
Tara can paint in 1 minute = 8/16 = 0.5 wall

∴ Working together, they can paint in 1 minute = 3 + 0.5 = 3.5 walls

∴ They can paint in 40 minutes = 3.5 × 40 = 140 walls

∴ Working together, Robin and Tara can paint 140 walls in 40 minutes.

১৩০.
A garrison of 400 men had food for 27 days. After 3 days a reinforcement of 200 men arrived. For how many more days will the remaining food last now?
  1. ক
    ক) 15 days
  2. খ
    খ) 16 days
  3. গ
    গ) 20 days
  4. ঘ
    ঘ) 22 days
সঠিক উত্তর: খ
খ) 16 days
উত্তর
সঠিক উত্তর: খ
খ) 16 days
খ
ব্যাখ্যা
Question: A garrison of 400 men had food for 27 days. After 3 days a reinforcement of 200 men arrived. For how many more days will the remaining food last now?

Solution:
After 3 days, food having for = 27 - 3 = 24 days
After arriving 200 men, total men = 400 + 200 = 600 men

400 men can eat the food for 24 days
1 man can eat the food for 24 × 400 days
600 men can eat the food for (24 × 400)/600 days
= 16 days
১৩১.
8 boys can finish a work in 8 days working 8 hours a day. How many hours should 4 boys have to work a day to finish the work in 8 days?
  1. ক
    ক) 12 hours
  2. খ
    খ) 16 hours
  3. গ
    গ) 20 hours
  4. ঘ
    ঘ) 17 hours
সঠিক উত্তর: খ
খ) 16 hours
উত্তর
সঠিক উত্তর: খ
খ) 16 hours
খ
ব্যাখ্যা
Question: 8 boys can finish a work in 8 days working 8 hours a day. How many hours should 4 boys have to work a day to finish the work in 8 days?

Solution: 
প্রথম অংশ থেকে পাই, ৮ জন বালক একটি কাজ ৮ দিনে শেষ করতে পারে দৈনিক ৮ ঘণ্টা কাজ করে।
এখানে, 
M1 = 8
D1 = 8
H1 = 8
W1 = 1

দ্বিতীয় অংশ থেকে পাই, ৪ জন বালক ৮ দিনে একই কাজ শেষ করতে দৈনিক কতক্ষণ কাজ করতে হবে?
এখানে, 
M2 = 4
D2 = 8
W2 = 1
H2 = ?

আমরা জানি,
M1 × W2 × D1 × H1 = M2 × W1 × D2 × H2
H2 = (M1 × W2 × D1 × H1) / (M2 × W1 × D2)
= (8 × 1 × 8 × 8) / (4 × 1 × 8)
= 16 hours
১৩২.
An industrial loom weaves 0.128 metres of cloth every second. Approximately, how many seconds will it take for the loom to weave 25 metres of cloth?
  1. ক
    ক) 195 seconds
  2. খ
    খ) 204 seconds
  3. গ
    গ) 255 seconds
  4. ঘ
    ঘ) 276 seconds
সঠিক উত্তর: ক
ক) 195 seconds
উত্তর
সঠিক উত্তর: ক
ক) 195 seconds
ক
ব্যাখ্যা
Let the required time be x seconds
Then,
More metres, More time (direct proportion)
∴ 0.128 : 25 :: 1 : x
x = 195.31
∴ Required time =195 seconds (approx)
১৩৩.
Nikki is 25% more efficient than Tina. Tina alone can build a craft in 20 days. Find the number of days taken by Nikki to finish the same piece of work?
  1. ক
    ক) 16
  2. খ
    খ) 17
  3. গ
    গ) 18
  4. ঘ
    ঘ) 19
সঠিক উত্তর: ক
ক) 16
উত্তর
সঠিক উত্তর: ক
ক) 16
ক
ব্যাখ্যা
The ratio of times taken by Tina and Nikki
= 125 : 100
= 5: 4.
Suppose Nikki takes x days to do the work.
5 : 4 = 20 : x
so, 5x= (4 x 20)
or, 5x = 80
       x= 80/5
      x =16 days
১৩৪.
In a school, there is a meal for 150 teachers or 250 students. If 180 students have taken the meal, how many teachers will be able to do with remaining meal?
  1. ক
    51
  2. খ
    47
  3. গ
    45
  4. ঘ
    42
সঠিক উত্তর: ঘ
42
উত্তর
সঠিক উত্তর: ঘ
42
ঘ
ব্যাখ্যা
question: In a school, there is a meal for 150 teachers or 250 students. If 180 students have taken the meal, how many teachers will be able to do with remaining meal?

Solution:
here,
250 students  = 150 teachers.
if 180 students have taken their meal.
the ramaining meal will cover = (250 - 180) = 70 students

∴ 70 students are equal to = (70 × 150)/250 teachers
= 42 teachers
১৩৫.
While working 7 hour a day, A alone can complete a piece of work in 6 days and B alone in 8 days . In what time would they complete it together, 8 hour a day?
  1. ক
    ক) 5 days
  2. খ
    খ) 3 days
  3. গ
    গ) 4 days
  4. ঘ
    ঘ) 3.6 days
সঠিক উত্তর: খ
খ) 3 days
উত্তর
সঠিক উত্তর: খ
খ) 3 days
খ
ব্যাখ্যা
A can complete the work in 7 × 6 = 42 hours
1 hour's work of A = 1/42

B can complete the work in 7 × 8 = 56 hours
1 hour's work of B = 1/56

(A + B)'s 1 hour's work
=1/42 + 1/56 = (4+3)/168 = 7/168

∴ Time taken by (A + B) working 8 hours daily
168/(7 × 8) = 3days
১৩৬.
55 men can finish a work in 42 days. How many additional men must be engaged to complete the work 9 days earlier?
  1. ক
    12 men
  2. খ
    15 men
  3. গ
    18 men
  4. ঘ
    20 men
সঠিক উত্তর: খ
15 men
উত্তর
সঠিক উত্তর: খ
15 men
খ
ব্যাখ্যা
Question: 55 men can finish a work in 42 days. How many additional men must be engaged to complete the work 9 days earlier?

Solution:
Here,
Days needed = (42 - 9) = 33 days

To complete the work in 42 days, it requires 55 men
To complete the work in 1 days, it requires (55 × 42) men
To complete the work in 33 days, it requires (55× 42)/33 men
= 70 men

∴ additional men required = (70 - 55) men
= 15 men
১৩৭.
Today is the day before sunday, after 72 days it will  be-
  1. ক
    Monday
  2. খ
    Sunday
  3. গ
    Wednesday
  4. ঘ
    Friday
  5. ঙ
    Saturday 
সঠিক উত্তর: ক
Monday
উত্তর
সঠিক উত্তর: ক
Monday
ক
ব্যাখ্যা
Question: Today is the day before sunday, after 72 days it will  be-

Solution:
Now, today is the day before Sunday.
So, today is Saturday

again,
To find the day after 72 days, we will divide 72 by 7 (since there are 7 days in a week)
=72/7 = 10 week 2 days
Then,
we will move 2 days forward from Saturday.
The correct sequence is saturday > sunday > monday

So, after 72 days it will  be Monday. 
১৩৮.
X can complete 1/3 of a work in 5 days and Y can complete 2/5 of a work in 10 days. In how many days both X and Y together can complete the work? 
  1. ক
    ক) 77/8 days
  2. খ
    খ) 75/8 days
  3. গ
    গ) 79/8 days
  4. ঘ
    ঘ) 81/8 days
সঠিক উত্তর: খ
খ) 75/8 days
উত্তর
সঠিক উত্তর: খ
খ) 75/8 days
খ
ব্যাখ্যা
X can complete 1/3 of a work in 5 days
X can complete whole work in 5 × 3 days
                                                  = 15 days 

Y can complete 2/5 of a work in 10 days
Y can complete whole work in (10× 5)/2 days
                                                 = 25 days

X's 1 day's work = 1/15 
Y's 1 day's work =1/25
(X +  Y)'s 1 day's work =(1/15) + (1/25)
                                    = (5 + 3)/75
                                    = 8/75 
X and Y together can complete the work in 75/8 days

১৩৯.
Bill and Ben can clean the garage together in 6 hours. If it takes Bill 10 hours working alone, how long will it take Ben working alone?
  1. ক
    ক) 4 hours
  2. খ
    খ) 11 hours
  3. গ
    গ) 15 hours
  4. ঘ
    ঘ) 16 hours
সঠিক উত্তর: গ
গ) 15 hours
উত্তর
সঠিক উত্তর: গ
গ) 15 hours
গ
ব্যাখ্যা

দুই জন একত্রে ১ ঘণ্টায় কাজ করতে পারে ১/৬ অংশ।
বিল ১ ঘণ্টায় কাজ করতে পারে ১/১০ অংশ।
বেন ১ ঘণ্টায় কাজ করতে পারে (১/৬ - ১/১০) = ২/৩০ = ১/১৫ অংশ।
∴ বেন একা পুরো কাজটি করতে পারবে  = ১৫ দিনে

১৪০.
If 5 workers can paint a house in 8 hours, how long would it take 20 workers to paint the same house?
  1. ক
    2 hours
  2. খ
    3 hours
  3. গ
    5 hours
  4. ঘ
    1 hour
সঠিক উত্তর: ক
2 hours
উত্তর
সঠিক উত্তর: ক
2 hours
ক
ব্যাখ্যা

Question: If 5 workers can paint a house in 8 hours, how long would it take 20 workers to paint the same house?

Solution:
 5 workers can paint a house in 8 hours
∴ 1 worker would take = (8 × 5) hours
∴ 20 workers would take = (8 × 5)/20 hours
= 2 hours

১৪১.
X, Y and Z can do a piece of work in 6 hours. X and Y can do the work in 8 hours and Y and Z can do the same work in 12 hours. In how many time will X and Z do the work?
  1. ক
    ক) 6 hours
  2. খ
    খ) 8 hours
  3. গ
    গ) 10 hours
  4. ঘ
    ঘ) 12 hours
সঠিক উত্তর: খ
খ) 8 hours
উত্তর
সঠিক উত্তর: খ
খ) 8 hours
খ
ব্যাখ্যা

x + y + z can do 1/6 part of the job in one hour……(i)
x + y can do 1/8 part of the job in one hour……(ii)
and, y + z can do 1/12 part of the job in one hour……(iii)
(ii) + (iii),
x + y + y + z = 1/8 + 1/12
Or, x + z + 2y = 5/24 ........ (iv)
Subtracting (i) from (iv) we get,
y = 5/24 - 1/6 = 1/24
Substituting the value of y in (iv) we get,
x + z + 2/24 = 5/24
x + z = 5/24 - 2/24 = 3/24 = 1/8
Hence x and z will do 1/8 of the job in one hour
So, x and z will do all of the work in 8 hours

১৪২.
If 8 men can reap 80 hectares in 24 days, how many hectares can 36 men reap in 30 days?
  1. ক
    450
  2. খ
    350
  3. গ
    152
  4. ঘ
    652
সঠিক উত্তর: ক
450
উত্তর
সঠিক উত্তর: ক
450
ক
ব্যাখ্যা
Question: If 8 men can reap 80 hectares in 24 days, how many hectares can 36 men reap in 30 days?

Solution:
৮ জন ২৪ দিনে ফসল কাটে ৮০ হেক্টর
∴ ৮ জন ১ দিনে ফসল কাটে ৮০/২৪ হেক্টর
∴ ১ জন ১ দিনে ফসল কাটে ৮০/(২৪ × ৮) হেক্টর
∴ ৩৬ জন ৩০ দিনে ফসল কাটে (৮০ × ৩৬ × ৩০)/(২৪ × ৮) হেক্টর
= ৪৫০ হেক্টর
১৪৩.
24 men can complete a piece of work in 24 days. In how many days can 36 men complete the same piece of work ?
  1. ক
    18 days
  2. খ
    16 days
  3. গ
    14 days
  4. ঘ
    21 days
সঠিক উত্তর: খ
16 days
উত্তর
সঠিক উত্তর: খ
16 days
খ
ব্যাখ্যা
Question: 24 men can complete a piece of work in 24 days. In how many days can 36 men complete the same piece of work ?

Solution: 
24 men can do in 24 days
1 man can do in = (24 × 24) days
36 men can do in = (24 × 24)/36 days
= 16 days
১৪৪.
When A, B and C are deployed for a task , A and B together do 70% of the work and B and C together do 50% of the work. Who is most efficient?
  1. ক
    ক) A
  2. খ
    খ) B
  3. গ
    গ) C
  4. ঘ
    ঘ) A & B equally efficient
  5. ঙ
    ঙ) Can't be determined
সঠিক উত্তর: ক
ক) A
উত্তর
সঠিক উত্তর: ক
ক) A
ক
ব্যাখ্যা

A + B = 70%
B + C = 50%
[∵ (A + B) + (B + C) − (A + B + C) = B]
=> B = 20% ; A = 50% and C = 30%
Hence A is most efficient.

১৪৫.
Ken left a job paying $ 75,000 per year to accept a sales job paying $ 45,000 per year plus 15 percent commission. If each of his sales is for $ 750, what is the least number of sales he must make per year if he is not to lose money because of the change?
  1. ক
    40
  2. খ
    200
  3. গ
    266
  4. ঘ
    267
সঠিক উত্তর: ঘ
267
উত্তর
সঠিক উত্তর: ঘ
267
ঘ
ব্যাখ্যা
Question: Ken left a job paying $ 75,000 per year to accept a sales job paying $ 45,000 per year plus 15 percent commission. If each of his sales is for $ 750, what is the least number of sales he must make per year if he is not to lose money because of the change?

Solution:
In order not to lose money because of the change Ken's total commission must be at least $ 75,000 - $ 45,000 = $ 30,000,
so total sales must be at least $ 30,000/0.15 = $200,000.

Which means that he must make at least $ 200,000/750 = 800/3 = 266.6 sales ≈ 267 sales.
১৪৬.
45 toymakers can prepare 30 toys per day. Raj wants 360 toys. How many toymakers should he employ to get the job done in 12 days?
  1. ক
    39
  2. খ
    45
  3. গ
    42
  4. ঘ
    35
সঠিক উত্তর: খ
45
উত্তর
সঠিক উত্তর: খ
45
খ
ব্যাখ্যা
Question: 45 toymakers can prepare 30 toys per day. Raj wants 360 toys. How many toymakers should he employ to get the job done in 12 days?

Solution:
Let, the required number of toymakers x
45 toymakers make 30 toys per day
So, 1 toymaker makes = 30/45 = 2/3 toys per day
Each toymaker in 12 days makes = (2/3) × 12 = 8 toys
So, x toymakers will make = 8x toys

ATQ,
8x = 360
⇒ x = 360 × (1/8)
∴ x = 45
১৪৭.
A certain number of artisans can complete a shoe fabrication consignment in 16 days. 8 additional artisans had to be deployed for the same consignment and together they completed it in 4 days less than the earlier estimate. The number of artisans initially employed was -
  1. ক
    ক) 18
  2. খ
    খ) 20
  3. গ
    গ) 24
  4. ঘ
    ঘ) 28
সঠিক উত্তর: গ
গ) 24
উত্তর
সঠিক উত্তর: গ
গ) 24
গ
ব্যাখ্যা

Let,
The original number of artisans be x.
More artisans, Less days [Indirect proportion]
∴ (x + 8) : x :: 16 : 12
⇒ 12 (x + 8) = 16x
⇒ 12x + 96 = 16x
⇒ 16x - 12x = 96
⇒ 4x = 96
⇒ x = 96/4
⇒ x = 24.

১৪৮.
A is thrice as good a workman as B and so takes 40 days less than B for doing a job. The time in which they can do the job together is - 
  1. ক
    30 days
  2. খ
    14 days
  3. গ
    15 days
  4. ঘ
    24 days
সঠিক উত্তর: গ
15 days
উত্তর
সঠিক উত্তর: গ
15 days
গ
ব্যাখ্যা

Question: A is thrice as good a workman as B and so takes 40 days less than B for doing a job. The time in which they can do the job together is - 

Solution:
Let A alone takes x days 
and B alone takes 3x days to complete the job.

ATQ,
3x - x = 40
⇒ 2x = 40
⇒ x = 20

So, A alone takes 20 days and B alone takes 3 × 20 = 60 days to complete the job.

(A + B)'s 1 days work = (1/20 + 1/60) = 1/15 part

∴ A and B together can do the work in 15 days.

১৪৯.
If 12 men can do a piece of work in 14 days, the time taken by 14 men to do the same piece of work will be - 
  1. ক
    10 days
  2. খ
    12 days
  3. গ
    14 days
  4. ঘ
    16 days
সঠিক উত্তর: খ
12 days
উত্তর
সঠিক উত্তর: খ
12 days
খ
ব্যাখ্যা

Question: If 12 men can do a piece of work in 14 days, the time taken by 14 men to do the same piece of work will be - 

Solution: 
from 12 men can do a piece of work in 14 days, we get - 
M1 = 12
D1 = 14

The time taken by 14 men to do the same piece of work will be
M2 = 14
D2 = ?

we know that,
M1 × D1 = M2 × D2
D2 = (12 × 14)/14
∴ D2 = 12 days

১৫০.
A fort has enough food for 360 soldiers for 120 days. After 40 days, 120 soldiers leave. For how many more days will the remaining food last.
  1. ক
    140 days
  2. খ
    80 days
  3. গ
    100 days
  4. ঘ
    120 days
সঠিক উত্তর: ঘ
120 days
উত্তর
সঠিক উত্তর: ঘ
120 days
ঘ
ব্যাখ্যা

Question: A fort has enough food for 360 soldiers for 120 days. After 40 days, 120 soldiers leave. For how many more days will the remaining food last.

Solution:
After 40 days: 360 soldiers had food for 80 days. Suppose 240 soldiers had food for x days.
Now, fewer soldiers, more days (Indirect Proportion):
240 : 360 : : 80 : x
⇒ 240/360 = 80/x
⇒ 240x = 360 × 80
⇒ x = (360 × 80)/240
∴ x = 120

১৫১.
Rakib can do a job in 15 minutes and his brother takes twice as long to do the same job. If they work together, how long it takes to complete the job?
  1. ক
    5 minutes
  2. খ
    7.5 minutes
  3. গ
    10 minutes
  4. ঘ
    12.5 minutes
সঠিক উত্তর: গ
10 minutes
উত্তর
সঠিক উত্তর: গ
10 minutes
গ
ব্যাখ্যা
Question: Rakib can do a job in 15 minutes and his brother takes twice as long to do the same job. If they work together, how long it takes to complete the job?

Solution: 
রাকিবের সময় লাগে ১৫ মিনিট 
তার ভাইয়ের সময় লাগে ৩০ মিনিট 

১ মিনিটে তারা কাজ সম্পন্ন করে = (১/১৫) + (১/৩০)
= (২ + ১)/৩০ 
= ৩/৩০ 
= ১/১০ অংশ 

∴ সম্পূর্ণ কাজ করতে সময় লাগে = ১০ মিনিট
১৫২.
5 person can do a work in 8 days working 7 hours a day. If 2 new persons join the team to complete the work in 4 days, they have to work per day for -
  1. ক
    ক) 10 hours
  2. খ
    খ) 12 hours
  3. গ
    গ) 15 hours
  4. ঘ
    ঘ) 8 hours
সঠিক উত্তর: ক
ক) 10 hours
উত্তর
সঠিক উত্তর: ক
ক) 10 hours
ক
ব্যাখ্যা
Question: 5 people can do a work in 8 days working 7 hours a day. If 2 new people join the team to complete the work in 4 days, they have to work per day for -

Solution: 
প্রশ্নের প্রথম অংশ - ৫ জন লোক একটি কাজ দৈনিক ৭ ঘন্টা কাজ করে ৮ দিনে শেষ করে।
এখানে, 
লোক, M1 = 5,
কাজ, W1 = 1,
দিন, D1 = 8,
সময়, H1 = 7.

প্রশ্নের দ্বিতীয় অংশ থেকে - যদি অতিরিক্ত ২ জন লোক যুক্ত করা হয় তাহলে একই কাজ ৪ দিনে শেষ করতে সবার প্রতিদিন কতক্ষণ কাজ করতে হবে?
এখানে,
লোক, M2 = 5 + 2 = 7,
কাজ, W2 = 1,
দিন, D2 = 4,
সময়, H2 = ?

আমরা জানি,
M1 × W2 × D1 × H1 = M2 × W1 × D2 × H2
H2 = (M1 × W2 × D1 × H1)/ (M2 × W1 × D2)
= (5 × 1 × 8 × 7)/(7 × 1 × 4)
= 280/28
= 10 hours
১৫৩.
John can paint 60 walls in 20 minutes. Emma can paint 9 walls in 15 minutes. Working together, how many walls can they paint in 25 minutes?
  1. ক
    65 walls
  2. খ
    90 walls
  3. গ
    75 walls
  4. ঘ
    95 walls
সঠিক উত্তর: খ
90 walls
উত্তর
সঠিক উত্তর: খ
90 walls
খ
ব্যাখ্যা
Question: John can paint 60 walls in 20 minutes. Emma can paint 9 walls in 15 minutes. Working together, how many walls can they paint in 25 minutes?

Solution:
John can paint in 1 min = 60/20 = 3 walls
Emma can paint in 1 min = 9/15 = 3/5 walls

∴ Working together they can paint in 1 min = (3 + 3/5) = 18/5 walls

∴ They can paint in 25 min = (18 × 25)/5 = 90 walls

So John and Emma can paint 90 walls together in 25 minutes.
১৫৪.
Hasan can paint 54 walls in 27 minutes. Rafiq can paint 25 walls in 10 minutes. Working together, how many walls can they paint in 20 minutes?
  1. ক
    60 walls
  2. খ
    70 walls
  3. গ
    90 walls
  4. ঘ
    100 walls
সঠিক উত্তর: গ
90 walls
উত্তর
সঠিক উত্তর: গ
90 walls
গ
ব্যাখ্যা

Question: Hasan can paint 54 walls in 27 minutes. Rafiq can paint 25 walls in 10 minutes. Working together, how many walls can they paint in 20 minutes?

Solution:
Hasan can paint in 1 minute = 54 ÷ 27 = 2 walls

Rafiq can paint in 1 minute = 25 ÷ 10 = 25/10 = 5/2 walls

∴ Together they can paint in 1 minute = 2 + (5/2) walls
= (4 + 5)/2 = 9/2 walls

∴ In 20 minutes, they can paint = (9/2) × 20 walls
= (9 × 20)/2
= 90 walls

১৫৫.
A can complete a task in 10 days, and B in 15 days. They work together for 5 days. What portion of the work remains?
  1. ক
    7/9
  2. খ
    1/5
  3. গ
    2/5
  4. ঘ
    1/6
সঠিক উত্তর: ঘ
1/6
উত্তর
সঠিক উত্তর: ঘ
1/6
ঘ
ব্যাখ্যা
Question: A can complete a task in 10 days, and B in 15 days. They work together for 5 days. What portion of the work remains?

Solution:
'A' 10 দিনে করতে পারে কাজটির 1 অংশ
'A' 1 দিনে করতে পারে কাজটির 1/10 অংশ

'B' 15 দিনে করতে পারে কাজটির 1 অংশ
'B'1 দিনে করতে পারে কাজটির 1/15 অংশ

(A ও B) 1 দিনে করতে পারে কাজটির (1/10) + (1/15) অংশ
= (3 + 2)/30 অংশ
= 5/30 অংশ
= 1/6 অংশ

(A ও B) 5 দিনে করতে পারে কাজটির = 5/6 অংশ


∴ কাজ বাকি থাকে = 1 - (5/6) অংশ
= (6 - 5)/6 অংশ
= 1/6 অংশ
১৫৬.
If 16 men working 7 hours a day can plow a field in 48 days, in how many days will 14 men working 12 hours a day plow the same field?
  1. ক
    46
  2. খ
    35
  3. গ
    32
  4. ঘ
    30
সঠিক উত্তর: গ
32
উত্তর
সঠিক উত্তর: গ
32
গ
ব্যাখ্যা
Question: If 16 men working 7 hours a day can plow a field in 48 days, in how many days will 14 men working 12 hours a day plow the same field?

Solution:
Let the one-day work = number of men ×  total working hours per day
Now, the ratio of total work = (14 × 12) : (16 × 7)
Now, the ratio of days = 48 : x
Where x is the required number of days
Now,
one day work is inversely proportional to the number of days:
So, (14 × 12) : (16 × 7) = 48: x
Or, x = (48 ×16 × 7)/ (14 × 12) = 32

Therefore, 32 days are required to plow the same field.
১৫৭.
Mina is 25% more efficient than Rina. Rina alone can build a craft in 20 days. Find the number of days taken by Mina to finish the same piece of work?
  1. ক
    ক) 18 days
  2. খ
    খ) 20 days
  3. গ
    গ) 16 days
  4. ঘ
    ঘ) 14 days
সঠিক উত্তর: গ
গ) 16 days
উত্তর
সঠিক উত্তর: গ
গ) 16 days
গ
ব্যাখ্যা
The ratio of times taken by Rina and Mina
= 125 : 100
= 5: 4.
Suppose Mina takes x days to do the work.
5 : 4 = 20 : x
so, 5x= (4 x 20)
or, 5x = 80
       x= 80/5
      x =16 days
১৫৮.
4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 Days. In how many days will 10 women complete it?
  1. ক
    ক) 10 days
  2. খ
    খ) 20 days
  3. গ
    গ) 30 days
  4. ঘ
    ঘ) 40 days
  5. ঙ
    ঙ) 50 days
সঠিক উত্তর: ঘ
ঘ) 40 days
উত্তর
সঠিক উত্তর: ঘ
ঘ) 40 days
ঘ
ব্যাখ্যা

(4M + 6W) × 8 = (3M + 7W) × 10
=> M / W = 11 : 1
Now , (4 × 11 + 6 × 1) × 8 = 10 × 1 × T
=> T = 40 days

১৫৯.
P can build a wall in 24 days and Q can do it in 20 days. With help of R, they completed the work in 6 days. Find in how many days R alone can do the work.
  1. ক
    56/3 days
  2. খ
    44/5 days
  3. গ
    40/3 days
  4. ঘ
    29/4 days
সঠিক উত্তর: গ
40/3 days
উত্তর
সঠিক উত্তর: গ
40/3 days
গ
ব্যাখ্যা

Question: P can build a wall in 24 days and Q can do it in 20 days. With help of R, they completed the work in 6 days. Find in how many days R alone can do the work.

Solution:
P can do 1/24 part per day
Q can do 1/20 part per day
R can do per day = (1/6) - {(1/24) + (1/20)}
= (1/6) - (11/120)
= (20/120) - (11/120)
= 3/40
Time taken by R alone = 40/3 days

১৬০.
A metal sphere weighing 84 kilograms is melted and recast into 4,000 identical nails. Calculate the weight of each nail in grams.
  1. ক
    0.21 grams
  2. খ
    2.4 grams
  3. গ
    21 grams
  4. ঘ
    24 grams
সঠিক উত্তর: গ
21 grams
উত্তর
সঠিক উত্তর: গ
21 grams
গ
ব্যাখ্যা
Question: A metal sphere weighing 84 kilograms is melted and recast into 4,000 identical nails. Calculate the weight of each nail in grams.

Solution:
দেওয়া আছে,
ধাতুর বলের ওজন = 84 কেজি = 84 × 1000 = 84000 গ্রাম
পেরেকের সংখ্যা = 4000 টি 

এখন,
4000 পেরেকের ওজন = 84000 গ্রাম
∴ 1 টি পেরেকের ওজন = (84000/4000) গ্রাম = 21 গ্রাম
১৬১.
A and B together can do a piece of work in 20 days. A having worked for 10 days, B finishes the remaining work alone in 24 days. In how many days shall B finish the whole work alone?
  1. ক
    30 days
  2. খ
    36 days
  3. গ
    42 days
  4. ঘ
    48 days
সঠিক উত্তর: ঘ
48 days
উত্তর
সঠিক উত্তর: ঘ
48 days
ঘ
ব্যাখ্যা
Question: A and B together can do a piece of work in 20 days. A and B having worked for 10 days, B finishes the remaining work alone in 24 days. In how many days shall B finish the whole work alone?

Solution:
A and B together in 20 days can do a piece of work
A and B together in 1 days can do 1/20 part
A and B together in 10 days can do (1 × 10)/20 part
= 1/2 part

So remaining work = (1 - 1/2) part
= 1/2 part

ATQ,
B finishes 1/2 part in 24 days.
∴ B finishes 1 part in (24 × 2) days
= 48 days
১৬২.
Q. 31 - 60: Read the following questions carefully and choose the right answer.
৩১) A man can walk uphill at the rate of 2.5km/hr and downhill at the rate of 3.25km/hr. If the total time required walking a certain distance up the hill and return to the starting position is 4 hr 36 min, what is the distance he walked up the hill?
  1. ক
    ক) 3.5km
  2. খ
    খ) 4.5km
  3. গ
    গ) 5.5 km
  4. ঘ
    ঘ) 6.5 km
সঠিক উত্তর: ঘ
ঘ) 6.5 km
উত্তর
সঠিক উত্তর: ঘ
ঘ) 6.5 km
ঘ
ব্যাখ্যা
Let the distance he walked up the hill be x km.
So, the distance he walked down the hill is x km.
Now,
According to the question
x/2.5 + x/3.25 = 4 + 36/60
⇒ 10x/25 + 100x/325 = 23/5
⇒ (130x + 100x)/325 = 23/5
⇒ 230x = (23 × 325)/5
⇒ 230x = 23 × 65
x = 6.5
∴ the distance he walked up the hill is 6.5 km.
১৬৩.
How many times in a day, are the hands of a clock in straight line but opposite in direction?
  1. ক
    ক) 22
  2. খ
    খ) 24
  3. গ
    গ) 48
  4. ঘ
    ঘ) 20
সঠিক উত্তর: ক
ক) 22
উত্তর
সঠিক উত্তর: ক
ক) 22
ক
ব্যাখ্যা

The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. Because between 5 and 7 they point in opposite directions at 6 o'clock only.
So, in a day, the hands point in the opposite directions 22 times.

১৬৪.
5 machines, working 6 hours a day, can produce 300 units in 3 days. How many hours a day must 10 machines work to produce 300 units in 1 day?
  1. ক
    11 hours
  2. খ
    8 hours
  3. গ
    9 hours
  4. ঘ
    10 hours
সঠিক উত্তর: গ
9 hours
উত্তর
সঠিক উত্তর: গ
9 hours
গ
ব্যাখ্যা
Question: 5 machines, working 6 hours a day, can produce 300 units in 3 days. How many hours a day must 10 machines work to produce 300 units in 1 day?

Solution:
5 machines, working 6 hours a day, can produce 300 units in 3 days
Formula used: M1 × T1 = M2 × T2
Where M1 and M2 is machines and T1 and T2 is time

Let H hours be the number of hours required
Applying the above formula
⇒ 5 × 6 × 3 = 10 × 1 × H
⇒ 90 = 10H
⇒ H = 90/10
⇒ H = 9 hours
∴ 10 machines need to work 9 hours to complete the work in 1 day.
১৬৫.
A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is:
  1. ক
    ক) 30 days
  2. খ
    খ) 42 days
  3. গ
    গ) 45 days
  4. ঘ
    ঘ) 52 days
সঠিক উত্তর: খ
খ) 42 days
উত্তর
সঠিক উত্তর: খ
খ) 42 days
খ
ব্যাখ্যা
After 10 days : 150 men had food for 35 days.
Suppose 125 men had food for x days.
Now, Less men, More days (Indirect Proportion)
125 : 150 :: 35 : x
125x = 150 × 35
x = 42
১৬৬.
Ali, Liton, and Karim pooled their funds to buy a gift for a friend. Ali contributed Tk. 200 less than 1/3 of the cost of the gift and Liton contributed Tk. 200 more than 1/4 of the cost. If Karim contributed the remaining Tk. 1500, what was the cost of the gift?
  1. ক
    Tk. 4300
  2. খ
    Tk. 3600
  3. গ
    Tk. 3300
  4. ঘ
    Tk. 2400
সঠিক উত্তর: খ
Tk. 3600
উত্তর
সঠিক উত্তর: খ
Tk. 3600
খ
ব্যাখ্যা
Question: Ali, Liton, and Karim pooled their funds to buy a gift for a friend. Ali contributed Tk. 200 less than 1/3 of the cost of the gift and Liton contributed Tk. 200 more than 1/4 of the cost. If Karim contributed the remaining Tk. 1500, what was the cost of the gift?

Solution:
Let,
The cost of the gift be Tk. x
ALi contributed = x/3 - 200
Liton contributed = x/4 + 200
Karim contributed = 1500
all together equal to x.
x/3 + x/4 + 1500 = x
⇒ 7x/12 +1500 = x
⇒ 5x/12 = 1500
⇒ x = (12 × 1500)/5
⇒ x = 12 × 300
∴ x = 3600
১৬৭.
Sarah finishes 60% of a painting in 12 days. She then asks David to help and together they complete the remaining work in 4 days. How many days would David take to complete the whole painting alone?
  1. ক
    20 days
  2. খ
    18 days
  3. গ
    28 days
  4. ঘ
    25 days
সঠিক উত্তর: ক
20 days
উত্তর
সঠিক উত্তর: ক
20 days
ক
ব্যাখ্যা
Question: Sarah finishes 60% of a painting in 12 days. She then asks David to help and together they complete the remaining work in 4 days. How many days would David take to complete the whole painting alone?

Solution:
Sarah does 60% or 3/5 work in 12 days
in one day, she does 1/20 work
in 4 days, she does 1/5 work
work remaining = (2/5) - (1/5)
= 1/5 work
David does 1/5 parts in 4 days
he will complete the work in 20 days
১৬৮.
A and B together can dive a trench in 12 days, which A alone can dive in 30 days. In how long B alone can burrow it?
  1. ক
    18 days
  2. খ
    19 days
  3. গ
    20 days
  4. ঘ
    21 days
সঠিক উত্তর: গ
20 days
উত্তর
সঠিক উত্তর: গ
20 days
গ
ব্যাখ্যা
Question: A and B together can dive a trench in 12 days, which A alone can dive in 30 days. In how long B alone can burrow it?

Solution:
(A+B)'s 1 day work = 1/12,
A's 1 day work =1/30
∴ B's 1 day work = (1/12 - 1/30) = 3/60 = 1/20

Henceforth, B alone can dive the trench in 20 days.
১৬৯.
A, B, and C can complete a piece of work in 8, 12, and 24 days respectively. Working together, they will complete the same work in -
  1. ক
    6 days
  2. খ
    3 days
  3. গ
    8 days
  4. ঘ
    4 days
সঠিক উত্তর: ঘ
4 days
উত্তর
সঠিক উত্তর: ঘ
4 days
ঘ
ব্যাখ্যা
Question: A, B, and C can complete a piece of work in 8, 12, and 24 days respectively. Working together, they will complete the same work in -

Solution:
(A + B + C)'s 1 days work = 1/8 + 1/12 + 1/24 
= (3 + 2 + 1)/24
= 6/24
= 1/4

∴ A, B, and C together can complete the work in = 4 days
১৭০.
A, B and C can complete a piece of work in 6, 8 and 12 days respectively. Working together, they will complete the work in ____ .
  1. ক
    ক) 5/3 days
  2. খ
    খ) 7/3 days
  3. গ
    গ) 10/3 days
  4. ঘ
    ঘ) 8/3 days
সঠিক উত্তর: ঘ
ঘ) 8/3 days
উত্তর
সঠিক উত্তর: ঘ
ঘ) 8/3 days
ঘ
ব্যাখ্যা
Question: A, B and C can complete a piece of work in 6, 8 and 12 days respectively. Working together, they will complete the work in ____ .

Solution: 
A  1 দিনে করে কাজটির  =1/6 অংশ
B  1 দিনে করে কাজটির  =1/8 অংশ
C 1 দিনে করে কাজটির  =1/12 অংশ

A + B + C 1 দিনে করে কাজটির  =(1/6) + (1/8) + (1/12) অংশ 
                                                    = (4 + 3 + 2 )/24 অংশ
                                                   = 9/24 অংশ
                                                   = 3/8 অংশ
A + B + C 3/8 অংশ কাজ করে 1 দিনে 
A + B + C 1 (সম্পূর্ণ)অংশ কাজ করে (1 × 8)/3 দিনে 
                                                         = 8/3 দিনে
১৭১.
Mr. Pollob can do a job in 120 minutes, while his colleague can do the same job in 3 hours. How long will it take them to work together to finish the same job?
  1. ক
    70 minutes
  2. খ
    72 minutes
  3. গ
    75 minutes
  4. ঘ
    78 minutes
সঠিক উত্তর: খ
72 minutes
উত্তর
সঠিক উত্তর: খ
72 minutes
খ
ব্যাখ্যা
Question: Mr. Pollob can do a job in 120 minutes, while his colleague can do the same job in 3 hours. How long will it take them to work together to finish the same job?

Solution:
Mr. Pollob can do a job in 120 minutes = 2 hours
∴ Mr. Pollob can do in 1 hour = 1/2 portion of the job

His colleague can do in 1 hour = 1/3 portion of the job

Together they can do in 1 hour = 1/2 + 1/3 = 5/6 portion of the job

∴ Together they can do full job in (6/5) hour = (6 × 60)/5 minutes
= 72 minutes
১৭২.
30 men are engaged to a work by a contractor for 6 days. They work for 4 days but due to some reasons, only 50% of the work will be completed. How many more men should be engaged to work to complete the work in a given period of time?
  1. ক
    ক) 30 men
  2. খ
    খ) 35 men
  3. গ
    গ) 40 men
  4. ঘ
    ঘ) 60 men
সঠিক উত্তর: ক
ক) 30 men
উত্তর
সঠিক উত্তর: ক
ক) 30 men
ক
ব্যাখ্যা
Question: 30 men are engaged to a work by a contractor for 6 days. They work for 4 days but due to some reasons, only 50% of the work will be completed. How many more men should be engaged to work to complete the work in a given period of time?

Solution: 
১/২ অংশ কাজ ৪ দিনে করে ৩০ জন 
∴ ১/২ অংশ কাজ ১ দিনে করে ৩০ × ৪ জন 
∴ ১/২ অংশ কাজ ২ দিনে করে (৩০ × ৪)/২ জন
= ৬০ জন 

অতিরিক্ত  লোক লাগবে ৬০ - ৩০ জন
= ৩০ জন 
১৭৩.
When Rakib, Piyash and Niloy complete a task, Rakib and Piyash together do 70% of the work and Piyash and Niloy together do 50% of the work. who is the most efficient?
  1. ক
    ক) Rakib
  2. খ
    খ) Piyash
  3. গ
    গ) Niloy
  4. ঘ
    ঘ) Can't be determined
সঠিক উত্তর: ক
ক) Rakib
উত্তর
সঠিক উত্তর: ক
ক) Rakib
ক
ব্যাখ্যা
Question: When Rakib, Piyash and Niloy complete  a task, Rakib and Piyash together do 70% of the work and Piyash and Niloy together do 50% of the work. who is the most efficient?

Solution: 
রাকিব, পিয়াস একসাথে ৭০% কাজ করে।
পিয়াস,  নিলয় একসাথে করে ৫০%
রাকিব, পিয়াস ও নিলয় মিলে করে ১০০% কাজ 

পিয়াস করে = ৭০% + ৫০% - ১০০% কাজ 
= ২০% লাজ 

নিলয় করে  = ৫০% - ২০% 
= ৩০%

রাকিব করে = ৭০% - ২০% 
= ৫০% 

অর্থাৎ, রাকিব সবচেয়ে দক্ষ। 

১৭৪.
A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in:
  1. ক
    ক) 4 days
  2. খ
    খ) 6 days
  3. গ
    গ) 8 days
  4. ঘ
    ঘ) 12 days
  5. ঙ
    ঙ) None of these
সঠিক উত্তর: খ
খ) 6 days
উত্তর
সঠিক উত্তর: খ
খ) 6 days
খ
ব্যাখ্যা

Suppose A, B and C take x, x/2, x/3 days respectively to finish the work
Then,
1/x + 2/x + 3/x = 1/2
⇒ 6/x = 1/2
⇒ x = 12
So, B takes 12/2 = 6 days to finish the work.

১৭৫.
A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 A.M. while machine P is closed at 11 A.M. and the remaining two machines complete work. Approximately at what time will the work (to print one lakh books) be finished?
  1. ক
    11 : 30 A.M.
  2. খ
    12 noon
  3. গ
    12 : 30 P.M
  4. ঘ
    1 : 00 P.M
  5. ঙ
    None of these
সঠিক উত্তর: ঘ
1 : 00 P.M
উত্তর
সঠিক উত্তর: ঘ
1 : 00 P.M
ঘ
ব্যাখ্যা
Question: A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 A.M. while machine P is closed at 11 A.M. and the remaining two machines complete work. Approximately at what time will the work (to print one lakh books) be finished?

Solution:
(P + Q + R)'s 1 hour's work = (1/8 + 1/10 + 1/12) = 37/120
Work done by P, Q and R in 2 hours = (37/120) × 2 = 37/60

Remaining work = (1 - 37/60) = 23/60
(Q + R)'s 1 hour's work = (1/10 + 1/12) = 11/60

Now,
11/60 of the work is done by Q and R in 1 hour.
23/60 of work will be done by Q and R in (60/11) × (23/60) = 23/11 hours = 2.09 hours ≈ 2 hours

So, the work will be finished approximately 2 hours after 11 A.M., i.e., around 1 P.M.
১৭৬.
Bashir and Benejir can clean the garage together in 6 hours. If it takes Bashir 10 hours working alone, how long will it take Benejir working alone?
  1. ক
    ক) 12 days
  2. খ
    খ) 10 days
  3. গ
    গ) 15 days
  4. ঘ
    ঘ) 18 days
সঠিক উত্তর: গ
গ) 15 days
উত্তর
সঠিক উত্তর: গ
গ) 15 days
গ
ব্যাখ্যা
দুই জন একত্রে ১ ঘণ্টায় কাজ করতে পারে ১/৬ অংশ।
বশির  ১ ঘণ্টায় কাজ করতে পারে ১/১০ অংশ।
বেনেজির  ১ ঘণ্টায় কাজ করতে পারে (১/৬ - ১/১০) = ২/৩০ = ১/১৫ অংশ।
∴ বেনেজির একা পুরো কাজটি করতে পারবে  = ১৫ দিনে
১৭৭.
16 men can complete a work in 6 days. How many men are needed to complete the work in 8 days?
  1. ক
    8
  2. খ
    10
  3. গ
    12
  4. ঘ
    15
সঠিক উত্তর: গ
12
উত্তর
সঠিক উত্তর: গ
12
গ
ব্যাখ্যা
Question: 16 men can complete a work in 6 days. How many men are needed to complete the work in 8 days?

Solution:
In 6 days the work can be done by 16 men
In 1 day the work can be done by 16 × 6 men
In 8 days the work can be done by (16 × 6)/8 men
=12
১৭৮.
A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in-
  1. ক
    4 days
  2. খ
    6 days
  3. গ
    8 days
  4. ঘ
    12 days
  5. ঙ
    None of these
সঠিক উত্তর: খ
6 days
উত্তর
সঠিক উত্তর: খ
6 days
খ
ব্যাখ্যা
Question: A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in-

Solution:
Suppose A, B and C take x, x/2 and x/3 days respectively to finish the work.
Then,
1/x + 2/x + 3/x = 1/2
⇒ 6/x = 1/2
⇒ x/6 = 2
∴ x = 12

So, B takes (12/2) = 6 days to finish the work.
১৭৯.
Six printers working together can print 720 documents in 6 days. If 2 printers stop working, how many documents can the remaining printers print in 9 days? 
  1. ক
    1000
  2. খ
    1200
  3. গ
    700
  4. ঘ
    720
সঠিক উত্তর: ঘ
720
উত্তর
সঠিক উত্তর: ঘ
720
ঘ
ব্যাখ্যা

Question: Six printers working together can print 720 documents in 6 days. If 2 printers stop working, how many documents can the remaining printers print in 9 days? 

Solution:
6টি প্রিন্টার 6 দিনে প্রিন্ট করে = 720 টি ডকুমেন্ট
∴ 1টি প্রিন্টার 6 দিনে প্রিন্ট করে = 720/6 = 120টি ডকুমেন্ট
∴ 1টি প্রিন্টার 1 দিনে প্রিন্ট করে = 120/6 = 20টি ডকুমেন্ট

অবশিষ্ট প্রিন্টার = 6 - 2 = 4 টি

∴ 4টি প্রিন্টার 9 দিনে প্রিন্ট করবে = 20 × 4 × 9 = 720 টি ডকুমেন্ট

১৮০.
A, B, and C can complete a piece of work in 8, 12, and 24 days respectively. Working together, they will complete the same work in -
  1. ক
    ক) 6 days
  2. খ
    খ) 3 days
  3. গ
    গ) 8 days
  4. ঘ
    ঘ) 4 days
সঠিক উত্তর: ঘ
ঘ) 4 days
উত্তর
সঠিক উত্তর: ঘ
ঘ) 4 days
ঘ
ব্যাখ্যা
Question: A, B, and C can complete a piece of work in 8, 12, and 24 days respectively. Working together, they will complete the same work in -

Solution:
(A + B + C)'s 1 days work = 1/8 + 1/12 + 1/24 
= (3 + 2 + 1)/24
= 6/24
= 1/4

A, B, and C together can complete the work in = 4 days
১৮১.
Five boys or 9 girls can do a piece of work in 19 days.In how many days can 3 boys and 6 girls do this work?
  1. ক
    ক) 12
  2. খ
    খ) 14
  3. গ
    গ) 15
  4. ঘ
    ঘ) None
সঠিক উত্তর: গ
গ) 15
উত্তর
সঠিক উত্তর: গ
গ) 15
গ
ব্যাখ্যা

এখানে 9 জন বালিকা = 5 জন বালক
তাহলে 1 জন বালিকা = 5/9 জন বালক
সুতরাং 3 জন বালক + 6 জন বালিকা = 3 + 6×5/9 = 3 + 10/3 = 19/3 জন বালক।
প্রশ্নমতে,
5 জন বালক কাজটি করে 19 দিনে
1 জন বালক কাজটি করে 19×5 দিনে
19/3 জন বালক কাজটি করে = 19×5×3/19 = 15 দিনে।
অর্থাৎ 3 জন বালক এবং 6 জন বালিকা কাজটি একত্রে 15 দিনে করতে পারে।

১৮২.
A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work is -
  1. ক
    ক) 4 days
  2. খ
    খ) 6 days
  3. গ
    গ) 8 days
  4. ঘ
    ঘ) 18 days
সঠিক উত্তর: ক
ক) 4 days
উত্তর
সঠিক উত্তর: ক
ক) 4 days
ক
ব্যাখ্যা

Ratio of rates of working of A and B = 2:1
So, ratio of times taken = 1 : 2
∴ A's 1 day's work = (1/6);
B's 1 day's work = 1/12
(A + B)'s 1 day's work = (1/6) + (1/12)
= 3/12
= 1/4
So, A and B together can finish the work in 4 days.

১৮৩.
In a training camp, 18 men can eat 20kg of rice in 3 days. How long will 6 men take to eat 40kg of rice?
  1. ক
    ক) 20
  2. খ
    খ) 18
  3. গ
    গ) 32
  4. ঘ
    ঘ) 20
সঠিক উত্তর: খ
খ) 18
উত্তর
সঠিক উত্তর: খ
খ) 18
খ
ব্যাখ্যা
Question: In a training camp, 18 men can eat 20kg of rice in 3 days. How long will 6 men take to eat 40kg of rice?

Solution:
18 জন 20কেজি চাল খায় = 3দিনে
18 জন 1কেজি চাল খায় = 3/20দিনে
1 জন 1 কেজি চাল খায় = 3 × 18/20দিনে  
6 জন 1 কেজি চাল খায় = (3 × 18)/(20 × 6) দিনে  
6 জন 40 কেজি চাল খায় = (3 × 18 × 40)/(20 × 6)দিনে  
                                         = 18 দিনে
১৮৪.
A, B and C can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but C left 4 days before the completion of the work. In how many days was the work completed?
  1. ক
    9 days
  2. খ
    11 days
  3. গ
    12 days
  4. ঘ
    10 days
সঠিক উত্তর: খ
11 days
উত্তর
সঠিক উত্তর: খ
11 days
খ
ব্যাখ্যা
Question: A, B and C can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but C left 4 days before the completion of the work. In how many days was the work completed?

Solution:
One day's work of A, B, and C = (1/24) + (1/30) + (1/40) = 1/10.
C leaves four days before the work is completed, which means only A and B work during the last four days.
The work done by A and B together in the last four days is = 4 {(1/24) + (1/30)} = 3/10.

Remaining Work = 7/10, which was done by A,B and C in the initial number of days.
Number of days required for this initial work = 7 days.
Thus, the total numbers of days required = 4 + 7 = 11 days.
১৮৫.
If 9 workers can assemble a truck in 12 hours, how long would it take 6 workers to assemble the same truck?
  1. ক
    3 hours
  2. খ
    6 hours
  3. গ
    9 hours
  4. ঘ
    18 hours
  5. ঙ
    24 hours
সঠিক উত্তর: ঘ
18 hours
উত্তর
সঠিক উত্তর: ঘ
18 hours
ঘ
ব্যাখ্যা

Question: If 9 workers can assemble a truck in 12 hours, how long would it take 6 workers to assemble the same truck?

Solution: 

Here, M1 = 9, M2 = 6, W1 = W2 = 1, T1 = 12, T2 = ?

∴ (M1 × T1)/(M2 × T2) = W1/W2 
⇒ (9 × 12)/ (6 × T2) = 1
⇒ T2 = (9 × 12)/6 
⇒ T2 = 18

১৮৬.
A man and a boy received 6000 Tk. as wages for 5 days for the work they did together. The man's efficiency in the work was double that of the boy. What are the daily wages of the boy?
  1. ক
    400 Tk.
  2. খ
    300 Tk.
  3. গ
    600 Tk.
  4. ঘ
    800 Tk.
সঠিক উত্তর: ক
400 Tk.
উত্তর
সঠিক উত্তর: ক
400 Tk.
ক
ব্যাখ্যা
Question:  A man and a boy received 6000 Tk. as wages for 5 days for the work they did together. The man's efficiency in the work was double that of the boy. What are the daily wages of the boy?

Solution: 
Ratio of 1 day's work of man and boy = 2 : 1
Total wages of the boy = (6000 × 1/3)
= 2000 Tk.

∴ Daily wages of the boy= 2000/5 = 400Tk.
১৮৭.
If 1/Q > 1, which of the following must be true?
  1. ক
    1 < Q2
  2. খ
    Q2 > 2
  3. গ
    1 > Q2
  4. ঘ
    Q2 > 1
  5. ঙ
    Q < Q2
সঠিক উত্তর: গ
1 > Q2
উত্তর
সঠিক উত্তর: গ
1 > Q2
গ
ব্যাখ্যা

Question: If 1/Q > 1, which of the following must be true?

Solution:
Given, 1/Q > 1
Since 1/Q > 1 and 1 > 0,  we know that 1/Q is positive, hence Q must also be positive.

Now, multiply both sides of the inequality by Q :
Q × (1/Q) > Q × 1
⇒ 1 > Q
⇒ 1 × Q > Q × Q
⇒ Q > Q2
⇒ 1 > Q2 [Since 1 > Q and Q > Q2]

Therefore, 1 > Q2 must be true.

১৮৮.
In the beginning, Rakib works at a rate such that he can finish a piece of work in 24 hrs, but he only works at this rate for 16 hrs. After that, he works at a rate such that he can do the whole work in 18 hrs. If Rakib is to finish this work at a stretch, how many hours will he take to finish this work?
  1. ক
    12 hrs
  2. খ
    18 hrs
  3. গ
    11.5 hrs
  4. ঘ
    15 hrs
  5. ঙ
    22 hrs
সঠিক উত্তর: ঙ
22 hrs
উত্তর
সঠিক উত্তর: ঙ
22 hrs
ঙ
ব্যাখ্যা
Question: In the beginning, Rakib works at a rate such that he can finish a piece of work in 24 hrs, but he only works at this rate for 16 hrs. After that, he works at a rate such that he can do the whole work in 18 hrs. If Rakib is to finish this work at a stretch, how many hours will he take to finish this work?

Solution:
Rakib’s 16 hr work = 16/24 = 2/3.
Remaining work = 1 - 2/3
= 1/3.
Using work and time formula:
This will be completed in (1/3) ×18 = 6 hrs.
So, total time taken to complete work = 16 + 6= 22 hrs.
১৮৯.
A and B can do a piece of work in 20 days and 30 days respectively. They began to work together but A leaves after some time, and B completed the remaining work in 10 days. After how many days did A leave? 
  1. ক
    5 days 
  2. খ
    8 days 
  3. গ
    7 days 
  4. ঘ
    10 days 
সঠিক উত্তর: খ
8 days 
উত্তর
সঠিক উত্তর: খ
8 days 
খ
ব্যাখ্যা

Question: A and B can do a piece of work in 20 days and 30 days respectively. They began to work together but A leaves after some time, and B completed the remaining work in 10 days. After how many days did A leave?

 
Solution:
Work done by B in 10 days = (1/30 × 10) part
= 10/30
= 1/3 part

Remaining work = 1 - 1/3 = 2/3 part

(A + B)'s 1 day's work = (1/20 + 1/30) part
= (3/60 + 2/60) = 5/60
= 1/12 part

Now, 1/12 part work is done by (A + B) in 1 day
∴ 1 part work is done by (A + B) in 12 days

∴ 2/3 part work is done by (A + B) in = 12 × (2/3) = 8 days

∴

১৯০.
Anik and Shuvo are working on a special assignment. Anik needs 6 hours to type 32 pages on a computer and Shuvo needs 5 hours to type 40 pages. If both of them work together on two different computers, how much time is needed to type an assignment of 110 pages?
  1. ক
    ক) 7 hour 30 minutes
  2. খ
    খ) 8 hour 15 minutes
  3. গ
    গ) 7 hour 15 minutes
  4. ঘ
    ঘ) 8 hour 30 minutes
সঠিক উত্তর: খ
খ) 8 hour 15 minutes
উত্তর
সঠিক উত্তর: খ
খ) 8 hour 15 minutes
খ
ব্যাখ্যা

Pages typed by Anik in 1 hour = 32/6 = 16/3
Pages typed by Shuvo in 1 hour = 40/5 = 8

Pages typed by Anik and Shuvo in 1 hour = 16/3 + 8 = 40/3
Time taken to type 110 pages when Anik and Shuvo work together = 110 × 3 /40 = 33/4
= 8 (1/4) hours = 8 hour 15 minutes.

১৯১.
The volume of a cone is 300π cubic centimeters. If the radius of its base is 6 cm, what is the height of the cone?
  1. ক
    10 cm 
  2. খ
    25 cm
  3. গ
    30 cm
  4. ঘ
    12 cm
সঠিক উত্তর: খ
25 cm
উত্তর
সঠিক উত্তর: খ
25 cm
খ
ব্যাখ্যা

Question: The volume of a cone is 300π cubic centimeters. If the radius of its base is 6 cm, what is the height of the cone?

solution:
দেওয়া আছে,
কোণকের আয়তন, V = 300π ঘন সে.মি.
ভূমির ব্যাসার্ধ, r = 6 সে.মি.
ধরি, কোণকের উচ্চতা = h সে.মি.

আমরা জানি,
কোণকের আয়তন, V = 1/3 × π × r2 × h
∴ 300π = 1/3 × π × 62 × h
⇒ 300 = 1/3 × 36 × h (π উভয় পক্ষ থেকে বাদ দিয়ে)
⇒ 300 = 12h
⇒ h = 300 / 12
∴ h = 25 সে.মি.

অতএব, কোণকটির উচ্চতা = 25 সে.মি.

১৯২.
Two bicycles start at the same time from points A and B, moving toward each other. If the distance between A and B is 125 km and their speeds are 14 km/h and 11 km/h respectively then after how much time will they meet each other?
  1. ক
    3.5 hours
  2. খ
    4.5 hours
  3. গ
    5 hours
  4. ঘ
    2.5 hours
সঠিক উত্তর: গ
5 hours
উত্তর
সঠিক উত্তর: গ
5 hours
গ
ব্যাখ্যা
Question: Two bicycles start at the same time from points A and B, moving toward each other. If the distance between A and B is 125 km and their speeds are 14 km/h and 11 km/h respectively then after how much time will they meet each other?

Solution:
Given,
The distance between A and B = 125 km
Speed of 1st bicycle = 14 km/h
Speed of 2nd bicycle = 11 km/h

The bicycles are moving toward each other,
So their relative speed = (Speed of 1st bicycle + Speed of 2nd bicycle)
= (14 + 11) km/h
= 25 km/h

Time = (Distance ÷ relative speed)
= (125 ÷ 25) 
= 5 h
১৯৩.
Salman and Rasel both have the same efficiency of work. If Salman finishes half of the work in 9 days. How much time will Rasel need to finish the rest of the work?
  1. ক
    ক) 18 days
  2. খ
    খ) 4.5 days
  3. গ
    গ) 9 days
  4. ঘ
    ঘ) 21 days
সঠিক উত্তর: গ
গ) 9 days
উত্তর
সঠিক উত্তর: গ
গ) 9 days
গ
ব্যাখ্যা
Question: Salman and Rasel both have the same efficiency of work. If Salman finishes half of the work in 9 days. How much time will Rasel need to finish the rest of the work?

Solution: 
যেহেতু সালমান এবং রাসেল উভয়ের দক্ষতা একই, তাদের একটি কাজ করতে একই সময় লাগবে।
তাহলে রাসেলের বাকি অর্ধেক কাজ শেষ করতেও ৯ দিন লাগবে।
১৯৪.
The price of a loaf of bread was increased by 20%. How many leaves can be purchased now by the amount of money used to buy 300 loaves at the earlier price?
  1. ক
    ক) 240
  2. খ
    খ) 250
  3. গ
    গ) 280
  4. ঘ
    ঘ) 320
সঠিক উত্তর: খ
খ) 250
উত্তর
সঠিক উত্তর: খ
খ) 250
খ
ব্যাখ্যা
ধরি,
প্রতি পিস পাউরুটির পূর্বমূল্য ছিল 100 টাকা 
300 পিস পাউরুটির পূর্বমূল্য ছিল = (100 × 300) টাকা
                                                     = 30000 টাকা


20% বৃদ্ধিতে ,
প্রতি পিস পাউরুটির বর্তমানমূল্য ছিল = 100 + 20 টাকা 
                                                          = 120 টাকা 
বর্তমান মূল্যে 30000 টাকা দিয়ে পাউরুটি কেনা যাবে = 30000/120 টাকা 
                                                                                  = 250 টাকা
১৯৫.
12 women can complete a piece of work in 10 days. 10 men can complete the same work in 8 days. What is the ratio of the work capacity of one man to one woman?
  1. ক
    1 : 2
  2. খ
    3 : 2
  3. গ
    5 : 2
  4. ঘ
    10 : 7
সঠিক উত্তর: খ
3 : 2
উত্তর
সঠিক উত্তর: খ
3 : 2
খ
ব্যাখ্যা

Question: 12 women can complete a piece of work in 10 days. 10 men can complete the same work in 8 days. What is the ratio of the work capacity of one man to one woman?

Solution:
12 women can complete a piece of work in 10 days.
∴ 1 woman can complete a piece of work in 10 × 12 = 120 days.

∴ 1 Woman's 1 day's work = 1/(12 × 10) 
= 1/120
∴ One woman's 1 day's work = 1/120

Similarly, 
Men's 1 day's work = 1/(10 × 8) = 1/80
∴ One man's 1 day's work = 1/80

∴ Ratio of capacity of one man to one woman = (1/80) : (1/120)
= 120 : 80
= 3 : 2

১৯৬.
The mess charges for 35 students for 24 days in Tk 6300. In how many days will the mess charges be Tk 3375 for 25 students?
  1. ক
    16
  2. খ
    18
  3. গ
    20
  4. ঘ
    22
সঠিক উত্তর: খ
18
উত্তর
সঠিক উত্তর: খ
18
খ
ব্যাখ্যা
Question: The mess charges for 35 students for 24 days in Tk 6300. In how many days will the mess charges be Tk 3375 for 25 students?

Solution: 
Let C be the daily mess charge per student.
Given that mess charges for 35 students for 24 days is Tk 6300, the daily cost per student is = 6300/(35 × 24)
= 7.5 

Now, to find how many days mess charges will be Tk 3375 for 25 students, we can use the daily cost per student (C):

The total mess charges for 25 students in D days is 3375 = 25 × C × D
⇒ D = 3375/(25 × 7.5)
= 18
১৯৭.
To complete a work, A takes 50% more time than B. If together they take 18 days to complete the work, how much time shall B take to do it?
  1. ক
    20 days
  2. খ
    24 days
  3. গ
    30 days
  4. ঘ
    32 days
সঠিক উত্তর: গ
30 days
উত্তর
সঠিক উত্তর: গ
30 days
গ
ব্যাখ্যা
Question: To complete a work, A takes 50% more time than B. If together they take 18 days to complete the work, how much time shall B take to do it?

Solution:
Let B takes x days to complete the work
Then A will take 50% more i.e 150% of x days i.e 3/2x days.

So the one day work of A and B together will be
(1/x) +{1/(3/2x)} = 1/18
⇒ (1/x) + (2/3x) = 1/18
⇒ 5/3x = 1/18
⇒ x = 30
∴ B takes 30 days to complete the work.
১৯৮.
10 women can do a work in 8 days. 8 men can complete the same work in 7 days. What is the ratio between the capacity of a man and a woman?
  1. ক
    9 : 7
  2. খ
    11 : 5
  3. গ
    7 : 3
  4. ঘ
    10 : 7
সঠিক উত্তর: ঘ
10 : 7
উত্তর
সঠিক উত্তর: ঘ
10 : 7
ঘ
ব্যাখ্যা
Question: 10 women can do a work in 8 days. 8 men can complete the same work in 7 days. What is the ratio between the capacity of a man and a woman?

Question: 
(10 × 8) = 80 women can complete the work in 1 day.
∴ 1 woman's 1 day's work = 1/80 part

(8 × 7) = 56 men can complete the work in 1 day.
1 man's 1 day's work = 1/56 part

So, required ratio = 1/56 : 1/80
= (1/56)/(1/80)
= 80/56
= 10/7
= 10 : 7
১৯৯.
A mechanic repairs 4 cars in 5/3 hours. How many cars can he repair in 50 minutes?
  1. ক
    2
  2. খ
    4
  3. গ
    21/3
  4. ঘ
    6
সঠিক উত্তর: ক
2
উত্তর
সঠিক উত্তর: ক
2
ক
ব্যাখ্যা

Question: A mechanic repairs 4 cars in 5/3 hours. How many cars can he repair in 50 minutes?

Solution:
Here,
5/3 hours = (5/3) × 60 = 100 minutes

In 100 minutes, he repairs = 4 cars
In 1 minute, he repairs = 4/100 
So, in 50 minutes, he repairs = (4 × 50)/100
= 2 cars

২০০.
A, B and C can complete a piece of work in 14, 6 and 12 days respectively. Working together, they will complete the work in ________ .
  1. ক
    ক) 19/9 days
  2. খ
    খ) 9/28 days
  3. গ
    গ) 28/9 days
  4. ঘ
    ঘ) 25/8 days
সঠিক উত্তর: গ
গ) 28/9 days
উত্তর
সঠিক উত্তর: গ
গ) 28/9 days
গ
ব্যাখ্যা
A  1 দিনে করে কাজটির  =1/14 অংশ
B  1 দিনে করে কাজটির  =1/6 অংশ
C 1 দিনে করে কাজটির  =1/12 অংশ

A + B + C 1 দিনে করে কাজটির  =(1/14) + (1/6) + (1/12) অংশ 
                                                    = (6 + 14 + 7 )/84 অংশ
                                                   = 27/84 অংশ
                                                   = 9/28 অংশ
A + B + C 9/28 অংশ কাজ করে 1 দিনে 
A + B + C 1 (সম্পূর্ণ)অংশ কাজ করে (1 × 28)/9 দিনে 
                                                         = 28/9 দিনে