Time & Work, Chain Rule

PrepBank · পাতা ৪ / ১১ · ৩০১–৪০০ / ১,০৭৬

৩০১.

50 workers can build 50 engines working 8 hours a day. How many workers need to be appointed extra to boost the production to double if they work 10 hours a days?

ক
20
খ
30
গ
40
ঘ
50

ব্যাখ্যা

Question: 50 workers can build 50 engines working 8 hours a day. How many workers need to be appointed extra to boost the production to double if they work 10 hours a days?

Solution:
8 hours to build 50 engines by 50 workers
1 hour to build 1 engine by = (50 × 8)/50 workers
10 hours to build 100 engine by = (8 × 100)/10 workers
= 80 workers

∴ extra workers = 80 - 50 = 30

৩০২.

A lift can carry 12 adults or 20 children at a time. If there are 9 adults in the lift, how many children can be loaded onto it?

ক
5
খ
6
গ
8
ঘ
10

ব্যাখ্যা

Question: A lift can carry 12 adults or 20 children at a time. If there are 9 adults in the lift, how many children can be loaded onto it?

Solution:
এখানে,
12 জন প্রাপ্তবয়স্ক (Adults) = 20 জন শিশু (Children)
∴ 1 জন প্রাপ্তবয়স্ক = 20 / 12 = 5/3 জন শিশু
∴ 9 জন প্রাপ্তবয়স্ক = 9 × 5/3 = 15 জন শিশু

লিফটের সর্বোচ্চ ধারণক্ষমতা = 20 জন শিশু
∴ আরও শিশু বহন করা যাবে = 20 - 15 = 5 জন শিশু

সুতরাং, 9 জন প্রাপ্তবয়স্কের সাথে আরও 5 জন শিশুকে লিফটে নেওয়া যাবে।

৩০৩.

A, B and C each working alone can complete a job in 8, 12 and 16 days respectively. If all three of them work together to complete the job and earn Tk. 3380, what will be C's share of the earnings?

ক
ক) Tk. 640
খ
খ) Tk. 780
গ
গ) Tk. 820
ঘ
ঘ) Tk. 830

ব্যাখ্যা

Question: A, B and C each working alone can complete a job in 8, 12 and 16 days respectively. If all three of them work together to complete the job and earn Tk. 3380, what will be C's share of the earnings?

Solution:
A, B এবং C 1 দিনে করতে পারে কাজটির 1/8,1/12, এবং 1/16 অংশ

A, B এবং C কাজের অনুপাত = 1/8 : 1/12 : 1/16
= (1/8) × 48 : (1/12) × 48 : (1/16) × 48
= 6 : 4 : 3
অনুপাতের রাশিগুলোর যোগফল = 6 + 4 + 3 = 13

C এর অংশ = 3380 এর 3/13 = 780

৩০৪.

Income of a company doubles after every one year. If the initial income was Tk. 4 lakhs, what would be the income after 5 years?

ক
Tk. 1.28 crores
খ
Tk. 1.24 crores
গ
Tk. 2.52 crores
ঘ
Tk. 2.56 crores

ব্যাখ্যা

Question: Income of a company doubles after every one year. If the initial income was Tk. 4 lakhs, what would be the income after 5 years?

Solution:
Initial income is 4 lakhs.
Income after 1 year = 4 × 2 = 8 lakhs.
Income after 2 years = 8 × 2 = 16 lakhs.
Income after 3 years = 16 × 2 = 32 lakhs.
Income after 4 years = 32 × 2 = 64 lakhs.
Income after 5 years = 64 × 2 = 128 lakhs = 1.28 crores.

৩০৫.

A work can be finished in 16 days by 20 women. The same work can be finished in 15 days by 16 men. The ratio between the efficiency of a man and a woman is -

ক
4 : 3
খ
2 : 1
গ
2 : 3
ঘ
1 : 3
ঙ
5 : 4

ব্যাখ্যা

Work done by 20 women in 1 day = 1/16
Work done by 1 woman in 1 day = 1/(16 × 20)

Work done by 16 men in 1 day = 1/15
Work done by 1 man in 1 day = 1/(15 × 16)
Efficiency of a man : efficiency of a woman
= 1/(15 × 16) : 1/(16 × 20)
= 1/15 : 1/20
= 1/3 : 1/4
= 4 : 3

৩০৬.

Adnan can do 1/5 of a work in 8 days. In how many days will he complete the work?

ক
20 days
খ
30 days
গ
40 days
ঘ
15 days
ঙ
25 days

ব্যাখ্যা

Question: Adnan can do 1/5 of a work in 8 days. In how many days will he complete the work?

Solution:
Adnan can do 1/5 of a work in 8 days.
∴ He will complete the work in = 8 × 5 = 40 days

∴ Adnan will complete the work in 40 days.

৩০৭.

50 persons can do a work in 12 day's by working 8 hours a day. Working how many hours per day can 60 persons finish the work in 16 days?

ক
ক) 8 hours
খ
খ) 6 hours
গ
গ) 5 hours
ঘ
ঘ) 4 hours

ব্যাখ্যা

50 persons can do a work in 12 day's by working 8 hours a day
1 person can do a work in 1 day's by working 8 × 50 × 12 hours a day
60 persons can do a work in 16 day's by working (8 × 50 × 12)/(60 × 12) hours a day = 5 hours a day

৩০৮.

75 employees have been able to finish only one-third of the project in 40 hours. The time committed by the management to complete the project was 90 hours. How many more employees should join the team to complete the project on time?

ক
45
খ
47
গ
49
ঘ
50
ঙ
51

ব্যাখ্যা

Remaining work = 1 - (1/3) = 2/3
Let number of more employees needed be E
Thus (75+E) employees complete 2/3 works in 50 hours.
∴ 75 employes × 40 hours × (2/3) = (75 + E) × 50 hours × (1/3)
∴ E = 45 = these many more employees are needed.

৩০৯.

A tower 17.5 m high casts a shadow of 40.25 m. What is the height of the building which casts a shadow 28.75 m long under similar conditions?

ক
10 m
খ
12.5 m
গ
17.2 m
ঘ
21.25 m

ব্যাখ্যা

Question: A tower 17.5 m high casts a shadow of 40.25 m. What is the height of the building which casts a shadow 28.75 m long under similar conditions?

Solution:
Let the height of the building is x
Now, the shadow ratio = building ratio
Height is directly proportional to shadow, so:
40.25 : 28.75 = 17.5 : x
Now, x = (28.75 × 17.5)/ 40.25 = 12.5 m

৩১০.

A truck can carry 24 motorcycles or 36 bicycles at a time. If there are 10 motorcycles on the truck, how many bicycles can be loaded along with them?

ক
20
খ
11
গ
21
ঘ
15
ঙ
None

ব্যাখ্যা

Question: A truck can carry 24 motorcycles or 36 bicycles at a time. If there are 10 motorcycles on the truck, how many bicycles can be loaded along with them?

Solution:
Here,
24 motorcycles = 36 bicycles
∴ 1 motorcycle = 36/24 bicycles = 3/2 bicycles

∴ 10 motorcycles = 10 × 3/2 = 15 bicycles

Total bicycle capacity = 36
∴ Remaining bicycles that can be loaded = 36 - 15 = 21 bicycles

∴ Required number of bicycles = 21

৩১১.

Hasan can dig 18 holes in 12 minutes. Faruk can dig the same number of holes in only 6 minutes. Hasan digs the first 9 holes, then Faruk digs for 2 minutes, and finally Hasan finishes the remaining holes. How long will it take them to dig 27 holes in total?

ক
10 minutes
খ
16 minutes
গ
18 minutes
ঘ
21 minutes

ব্যাখ্যা

Question: Hasan can dig 18 holes in 12 minutes. Faruk can dig the same number of holes in only 6 minutes. Hasan digs the first 9 holes, then Faruk digs for 2 minutes, and finally Hasan finishes the remaining holes. How long will it take them to dig 27 holes in total?

Solution:
Faruk can dig 18 holes in 6 minutes.
∴ In 2 minutes, he can dig = (18 × 2)/6 holes
= 6 holes

Hasan first digs 9 holes.

∴ Total completed = 9 (Hasan) + 6 (Faruk) = 15 holes
Remaining = 27 - 15 = 12 holes

Hasan can dig 18 holes in 12 minutes.
∴ To dig 12 holes, Hasan will take = (12 × 12) / 18 = 8 minutes

Time Hasan spent digging first 9 holes = (12 × 9)/18 = 6 minutes

∴ Total time = 6 (Hasan) + 2 (Faruk) + 8 (Hasan) = 16 minutes

৩১২.

4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weavers in 8 days?

ক
4 mats
খ
8 mats
গ
12 mats
ঘ
16 mats

ব্যাখ্যা

Question: 4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weavers in 8 days?

Solution:
4 mat-weavers in 4 days weave = 4 mats
∴ 1 mat-weavers in 1 days weave = 4/(4 × 4) mats
∴ 8 mat-weavers in 8 days weave = (4 × 8 × 8)/(4 × 4) mats
= 16 mats

৩১৩.

A 100 m long 3 m high and 30 cm wide wall is built by 30 men, 20 women and 50 children working 9 hours a day in 20 days. How long a wall 1.5 m high 30 cm wide can be built by 15 men, 25 women and 35 children working 2 hour a day in 15 days (given men, women and children are equally efficient)?

ক
75 m
খ
25 m
গ
50 m
ঘ
100 m
ঙ
125 m

ব্যাখ্যা

Question: A 100 m long 3 m high and 30 cm wide wall is built by 30 men, 20 women and 50 children working 9 hours a day in 20 days. How long a wall 1.5 m high 30 cm wide can be built by 15 men, 25 women and 35 children working 2 hour a day in 15 days (given men, women and children are equally efficient)?

Solution:
Earlier dimensions of the wall = 100 × 3 × 0.30.
Volume of the wall = 90
New dimensions = L × 1.5 × 0.3.
Volume of the wall = 0.45L
∴ As men, women and children are given to be equally efficient, so in the first case, the total number of persons is (30 + 20 + 50) = 100 and the same in the second case is (15 + 25 + 35) = 75

working 9 hours a day in 20 days 100 persons make 90 m³ wall
∴ working 1 hours a day in 1 days 1 persons make 90/(100 × 20 × 9) m³ wall
∴ working 2 hours a day in 15 days 75 persons make (90 × 75 × 15 × 2)/(100 × 20 × 9) m3 wall
= 11.25

∴ Length of the wall = L = 11.25/0.45 = 25 m

৩১৪.

A group of men decided to do a job in 6 days. But since 5 men dropped out every day, the job completed at the end of the 8th day. How many men were there at the beginning?

ক
90
খ
85
গ
70
ঘ
65

ব্যাখ্যা

Question: A group of men decided to do a job in 6 days. But since 5 men dropped out every day, the job completed at the end of the 8th day. How many men were there at the beginning?

Solution:
Let
x be the initial number of men then

ATQ,
6x = x + (x - 5) + (x - 10) + (x - 15) + (x - 20) + (x - 25) + (x - 30) + (x - 35)
⇒ 6x = 8x - 140
⇒ 2x = 140
⇒ x = 140/2
∴ x = 70

৩১৫.

A teacher has 3 hours to grade all the papers submitted by the 35 students in her class. She gets through the first 5 papers in 30 minutes. How much faster does she have to work to grade the remaining papers in the allotted time?

ক
ক) 10%
খ
খ) 15%
গ
গ) 20%
ঘ
ঘ) 16.67%

ব্যাখ্যা

প্রথম 5 টি copy এর প্রত্যেকটি দেখতে সময় লাগে = 30/5
= 6 মিনিট
পরের 30 টি copy এর প্রত্যেকটি দেখতে সময় পাবে = 150/30
= 5 মিনিট

বর্তমান রেট - 1/6
কাঙ্ক্ষিত রেট - 1/5
বাড়াতে হবে - 1/30

অতএব, {(1/30) / (1/6)} × 100
= 20% faster হতে হবে ।

৩১৬.

Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?

ক
648
খ
1800
গ
2700
ঘ
1080
ঙ
None

ব্যাখ্যা

Question: Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?

Solution:
৬টি মেশিন ১ মিনিটে বোতল বানায় ২৭০টি
১টি মেশিন ১ মিনিটে বোতল বানায় ২৭০/৬ = ৪৫টি
১০টি মেশিন ১ মিনিটে বোতল বানায় ৪৫ × ১০ = ৪৫০টি
১০টি মেশিন ৪ মিনিটে বোতল বানায় ৪৫০ × ৪ = ১৮০০টি

৩১৭.

A takes three times as long as B and C together to do a job. B takes four times as long as A and C together to do the work. If all three, working together can complete the job in 24 days, then the number of days, A alone will take to finish the job is =?

ক
86 days
খ
92 days
গ
95 days
ঘ
96 days

ব্যাখ্যা

Question: A takes three times as long as B and C together to do a job. B takes four times as long as A and C together to do the work. If all three, working together can complete the job in 24 days, then the number of days, A alone will take to finish the job is =?

Solution:
Let the time taken by B and C = x days
∴ Time taken by A = 3x days
∴ Part of the work done by A, B and C in 1 day = 1/x + 1/3x = (3 + 1)/3x = 4/3x

∴ 4/3x = 1/24
⇒ 3x = 4 × 24
⇒ x = 96/3
∴ x = 32 days

∴ Time taken by A = 32 × 3 = 96 days.

৩১৮.

3 pumps working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?

ক
8
খ
9
গ
10
ঘ
11
ঙ
12

ব্যাখ্যা

Question: 3 pumps working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?

Solution:
Let the required no of working hours per day be x.
More pumps , Less working hours per day (Indirect Proportion)
Less days, More working hours per day (Indirect Proportion)

∴ (4 × 1 × x) = (3 × 2 × 8)
⇒ x = 12

৩১৯.

The owner of a bike buys petrol for 3 years continuously at Tk. 64, Tk. 80 and Tk. 320 per litre respectively. If he spends Tk. 32,000 every year buying petrol, what is the average price per litre of petrol?

ক
Tk. 100
খ
Tk. 92
গ
Tk. 90
ঘ
Tk. 106
ঙ
Tk. 96

ব্যাখ্যা

Question: The owner of a bike buys petrol for 3 years continuously at Tk. 64, Tk. 80 and Tk. 320 per litre respectively. If he spends Tk. 32,000 every year buying petrol, what is the average price per litre of petrol?

Solution:
Number of litres consume of first year = 32000/64 = 500 litres
Number of litres consume of second year = 32000/80 = 400 litres
Number of litres consume of third year = 32000/320 = 100 litres
Total consume petrol in three years = 500 + 400 + 100 = 1000 litres
Total expenditure on petrol in three years = 32000 × 3
Average cost per litres of petrol = (32000 × 3)/1000 = Tk. 96

৩২০.

If A and B can together do a work in 15 days and B alone can finish the job in 20 days. In how many days, A alone can finish the job?

ক
ক) 60
খ
খ) 45
গ
গ) 40
ঘ
ঘ) 30
ঙ
ঙ) None of above

ব্যাখ্যা

A and B complete a work in = 15 days
One day's work of (A + B) = 1/15
B complete the work in = 20 days;
One day's work of B = 1/20
Then, A's one day's work = 1/15 - 1/20
= (4 - 3)/60
= 1/60
Thus, A can complete the work in = 60 days.

৩২১.

P, Q and R can do a job in 20, 30 and 60 days respectively. In how many days can P do the job if he is assisted by Q and R every third day?

ক
12 days
খ
11 days
গ
15 days
ঘ
13 days
ঙ
None

ব্যাখ্যা

Question: P, Q and R can do a job in 20, 30 and 60 days respectively. In how many days can P do the job if he is assisted by Q and R every third day?

Solution:
P's 2 days' work = 2/20
= 1/10

∴ (P + Q + R)'s 1 day's work
= (1/20 + 1/30 + 1/60)
= 6/60
= 1/10

∴ Job done in 3 days [P alone 2 days + (P+Q+R) 1 day] = (1/10 + 1/10) = 1/5

Now, 1/5 jobs is done in 3 days

∴ The whole job will be done in (3 x 5) = 15 days.

৩২২.

M did a piece of work in 5 days. That piece of work was done by N in 9 days. If M and N worked together, they got total wages of Tk. 4200. Find the share of N.

ক
Tk. 1500
খ
Tk. 2000
গ
Tk. 1000
ঘ
Tk. 1200
ঙ
None of these

ব্যাখ্যা

Question: M did a piece of work in 5 days. That piece of work was done by N in 9 days. If M and N worked together, they got total wages of Tk. 4200. Find the share of N.

Solution:
M's 1 day's work 1/5
N's 1 day's work 1/9

M : N
Time = 5 : 9
Efficiency = 9 : 5

(Time and efficiency are inversely proportional)
N gets = 4200 × (5/14)
= 1500

Thus, N gets the wages of Tk. 1500.

৩২৩.

Working individually, A would finish a project in 3 days. B takes double the time as taken by A, C takes one more day in addition to the time taken by B. If all three of them decide to work together on the project, how much time would they take to finish it?

ক
ক) 15/16 days
খ
খ) 11/10 days
গ
গ) 14/9 days
ঘ
ঘ) 16/7 days

ব্যাখ্যা

A can do the work in 3 days. So, in 1 day a does 1/3 amount of work.

B takes double the time as A. So, B can do the work in 6 days. So, in 1 day B does 1/6 amount of work

C takes one more day in addition to the time taken by B. So, C can do the work in 7 days. So, in 1 day C does 1/7 amount of work

When they work together, in 1 day they complete how much work?
In 1 day A, B and C together complete = 1/3 + 1/6 + 1/7 = 9/14 amount of work
A, B and C together complete the entire work in 14/9 days.

৩২৪.

A computer can perform 30 identical tasks in 6 hour. At that rate, what is the minimum number of computers that should be assigned to complete 80 of the tasks within 3 hours?

ক
ক) 12
খ
খ) 7
গ
গ) 6
ঘ
ঘ) 16

ব্যাখ্যা

We Know
Total work = rate × Time
Therefore, Rate = 30/6 = 5 task/hr

Now we need to find the number of computers
Given, total work = 80 task and total time = 3 hrs

So, No. of computers = 80 / (5×3) = 5.33, but no. of computers cannot be fraction, so we have to consider it as 1.
∴ Total no. of computers = 5+1 = 6.

৩২৫.

If the number of workers is doubled, how many times more time will be required to complete the task?

ক
0.5 times
খ
2 times
গ
3 times
ঘ
None of these

ব্যাখ্যা

Question: If the number of workers is doubled, how many times more time will be required to complete the task?

Solution:
ধরি,
শ্রমিক সংখ্যা = x, এর দিগুণ = 2x,
সময় = n
x জন কাজটি করে n সময়ে

১ জন কাজটি করে = xn সময়ে
২x জন কাজটি করে = xn/২x
= n/২ সময়ে বা ১/২ সময়ে।

৩২৬.

If 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days?

ক
ক) 1
খ
খ) 3
গ
গ) 7
ঘ
ঘ) 14
ঙ
ঙ) 16

ব্যাখ্যা

Let the required number of days be x.
Less spiders, More days (Indirect Proportion)
Less webs, Less days (Direct Proportion)
Spiders 1:7 and Webs 7:1 } :: 7:x
=> 1 × 7 × x = 7 × 1 × 7
=> x = 7

৩২৭.

The efficiency of A, B and C is in the ratio 4 : 5 : 6. Together they can complete a piece of work in 32 days. In how many days will B alone complete the work?

ক
ক) 96 days
খ
খ) 90 days
গ
গ) 98 days
ঘ
ঘ) 92 days

ব্যাখ্যা

Efficiency of A, B and C is in the ratio 4 : 5 : 6
They can complete a work in 32 days by working together

Calculation:
Total efficiency of all three working together = 4 + 5 + 6 = 15
Total work done in 32 days = 15 × 32

Let B will complete the work in n days, working alone
⇒ 5n = 15 × 32
⇒ n = 96

∴ B alone will complete the work in 96 days

৩২৮.

Abir does 80% of a work in 20 days. He then calls in Belal and they together finish the remaining work in 3 days. How long Belal alone would take to do the whole work?

ক
70 days days
খ
63/2 days days
গ
75/2 days days
ঘ
None of these

ব্যাখ্যা

Question: Abir does 80% of a work in 20 days. He then calls in Belal and they together finish the remaining work in 3 days. How long Belal alone would take to do the whole work?

Solution:
abir does 80% or 4/5 work in 20 days
in one day, he does 1/25 work
in 3 days, he does 3/25 work

work remaining = 1/5 - 3/25
= 2/25 work

Belal does 2/25 parts in 3 days
he will complete the work 75/2 days

৩২৯.

A is twice as good a workman as B and therefore can finish a job 30 days earlier than B. Working together, in how many days can they finish the job?

ক
35 days
খ
30 days
গ
25 days
ঘ
20 days

ব্যাখ্যা

Question: A is twice as good a workman as B and therefore can finish a job 30 days earlier than B. Working together, in how many days can they finish the job?

Solution:

Given,
A is twice as good workman as B. Means,
A = 2B
Let B can finish work in X days, then A will finish same work in (X - 30) days alone
Now,
BX = 2B × (X - 30)
⇒ BX = 2BX - 60B
∴ X = 60 days
B can finish work in 60 days, then A can finish the work in 30 days.
One day work of B = 1/60

One day work of A = 1/30

One day work of (A+B) = (1/60) + (1/30) ⇒ (1+2)/60 ⇒ 3/60 ⇒ 1/20

So, they can finish work together in 20 days.

৩৩০.

A group of women decided to do a job in 5 days. But since 15 women dropped out every day, the job completed at the end of the 8th day. How many women were there at the beginning?

ক
120
খ
130
গ
140
ঘ
145

ব্যাখ্যা

Question: A group of women decided to do a job in 5 days. But since 15 women dropped out every day, the job completed at the end of the 8th day. How many women were there at the beginning?

Solution:
Let X be the initial number of women then,
According to the question,
5X = X + (X - 15) + (X - 30) + (X - 45) + (X - 60) + (X - 75) + (X - 90) + (X - 105)
⇒ 5X = 8X - 420
⇒ 8X - 5X = 420
⇒ 3X = 420
⇒ X = 420/3
∴ X = 140 women

৩৩১.

10 men or 15 women can do a certain work in 5 days. if 5 men and 15 women work together, they can complete the work in -

ক
10/3 days
খ
10/7 days
গ
20/7 days
ঘ
15/4 days
ঙ
None of the above

ব্যাখ্যা

Question: 10 men or 15 women can do a certain work in 5 days. if 5 men and 15 women work together, they can complete the work in -

Solution:
10 men can do it in 5 days.
one man can do it in (5 × 10) = 50 days
in one day 1 man can do = 1/50
in one day 5 men can do = 5/50 = 1/10

15 women can do it in 5 days.
in one day they can do = 1/5

so, in one day, 5 men and 15 women together can do = 1/10 + 1/5
= 3/10

total time to complete the work is = 10/3 days

৩৩২.

Salman and Maruf can do a work together in 4 days. Tofail and Hemal can do the same work in 12 days. So, in how many days can all four complete that work together?

ক
4 days
খ
8 days
গ
3 days
ঘ
12 days

ব্যাখ্যা

Question: Salman and Maruf can do a work together in 4 days. Tofail and Hemal can do the same work in 12 days. So, in how many days can all four complete that work together?

Solution:
সালমান ও মারুফ ১ দিনে করে ১/৪ অংশ
তোফায়েল ও হিমেল ১ দিনে করে ১/১২ অংশ

৪ জন একত্রে ১ দিনে করে = ১/৪ + ১/১২ অংশ
= (৩ + ১)/১২ অংশ
= ৪/১২ অংশ
= ১/৩ অংশ

তারা একত্রে ১/৩ অংশ করে ১ দিনে
∴ তারা সম্পূর্ণ বা ১ অংশ করে ৩ দিনে।

৩৩৩.

A team of workers can finish a project in 20 days. However, when 5 of them were absent, it took 25 days to complete the same work. How many workers were originally assigned to the project?

ক
35 workers
খ
10 workers
গ
15 workers
ঘ
25 workers
ঙ
20 workers

ব্যাখ্যা

Question: A team of workers can finish a project in 20 days. However, when 5 of them were absent, it took 25 days to complete the same work. How many workers were originally assigned to the project?

Solution:
Let,
the total number of people working originally = x
When 5 people were absent,
Total present workers = x - 5

x workers can complete the work in 20 days
∴ 1 worker can complete it in 20x days
∴ (x - 5) workers can complete it in 20x/(x - 5) days

ATQ,
20x/(x - 5) = 25
⇒ 4x/(x - 5) = 5
⇒ 5x - 25 = 4x
∴ x = 25

∴ The total number of people working originally = 25

৩৩৪.

Apu was assigned to do 2 similar tasks. He completes the second task in two-thirds the time it takes him to complete the first task. If it took him an hour to complete both the tasks, in how many minutes did he complete the second task?

ক
20
খ
24
গ
30
ঘ
36
ঙ
None

ব্যাখ্যা

Question: Apu was assigned to do 2 similar tasks. He completes the second task in two-thirds the time it takes him to complete the first task. If it took him an hour to complete both the tasks, in how many minutes did he complete the second task?

Solution:
Let the time taken for the first task be t minutes.
Then, time for the second task = 2t/3 minutes.

Total time for both tasks = 1 hour = 60 minutes.

ATQ,
t + (2t/3) = 60
⇒ (3t + 2t)/3 = 60
⇒ 5t = 60 × 3
⇒ t = (60 × 3)/5
∴ t = 36

∴ Second task = 2t/3 = (2 × 36)/3 = 24 minutes

So Apu completed the second task in 24 minutes.

৩৩৫.

Robi and Kamal are working on an assignment. Robi takes 6 hours to type 32 pages on a computer, while Kamal takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?

ক
ক) 7 hours 30 minutes
খ
খ) 8 hours
গ
গ) 8 hours 15 minutes
ঘ
ঘ) 8 hours 25 minutes
ঙ
ঙ) None of these

ব্যাখ্যা

Number of pages typed by Robi in 1 hour = 32/6 = 16/3 .
Number of pages typed by Kamal in 1 hour = 40/5 = 8
Number of pages typed by both in 1 hour = (16/3 + 8) = 40/3
Therefore, Time taken by both to type 110 pages = 110/(40/3) hours
= 110 × 3/40 hours (or) 8 hours 15 minutes.

৩৩৬.

A does a work in 12 days, B in 15 days, and C can do half the work in 10 days. How long will it take them to complete the whole work if they work together?

ক
3 days
খ
5 days
গ
8 days
ঘ
12 days

ব্যাখ্যা

Question: A does a work in 12 days, B in 15 days, and C can do half the work in 10 days. How long will it take them to complete the whole work if they work together?

Solution:
A,
12 দিনে করে কাজটির = 1 অংশ
∴ 1 দিনে করে কাজটির = 1/12 অংশ

B,
15 দিনে করে কাজটির = 1 অংশ
∴ 1 দিনে করে কাজটির = 1/15 অংশ

C,
10 দিনে করে কাজটির = 1/2 অংশ
∴ 1 দিনে করে কাজটির = 1/20 অংশ

A, B ও C একত্রে করে = (1/12) + (1/15) + (1/20)
= (5 + 4 + 3)/60
= 12/60
= 1/5 অংশ

A, B ও C একত্রে 1/5 অংশ করে = 1 দিনে
∴ 1 বা সম্পূর্ণ অংশ করে = (1 × 5) দিনে
= 5 দিনে

৩৩৭.

Working alone, Protik takes complete April to build a pavement. His friend Mahmud is 25% faster than him at the same work. Working alone, how many days will Mahmud take to build the same pavement?

ক
ক) 20 days
খ
খ) 24 days
গ
গ) 22.5 days
ঘ
ঘ) 37.5 days

ব্যাখ্যা

April has 30 days. So Protik takes 30 days to build the pavement.
Mahmud is 25% faster than Protik

25% = 25/100 = .25
This means, if Protik is 1, then Mahmud is (1 + 0.25) = 1.25
Protik takes 30 days to do the work.
Mahmud will take = 30/1.24 = 24 days to get the work done.

৩৩৮.

If a quarter kg of carrots costs 60 poysa, how many poysa will 200 gms cost?

ক
ক) 78 poysa
খ
খ) 48 poysa
গ
গ) 54 poysa
ঘ
ঘ) 62 poysa
ঙ
ঙ) 65 poysa

ব্যাখ্যা

Quarter of Kg means 250 gm
Less weight, less price (Direct Proportion)
So, 250 : 200 :: 60 : x
=> x = 48
So 200 gm will cost 48 poysa.

৩৩৯.

Amir and Hannan working together can finish a work in 3 hours. If they work alone, Hannan takes 3 times as long as Amir. How long does Hannan take to finish the job alone?

ক
6
খ
12
গ
14
ঘ
16
ঙ
None

ব্যাখ্যা

Question: Amir and Hannan working together can finish a work in 3 hours. If they work alone, Hannan takes 3 times as long as Amir. How long does Hannan take to finish the job alone?

Solution:
ধরি,
আমির একা কাজটি শেষ করতে সময় নেয় = x ঘণ্টা
হান্নান একা কাজটি শেষ করতে সময় নেয় = 3x ঘণ্টা

এখন
আমিরের 1 ঘণ্টায় কাজের পরিমাণ = 1/x
হান্নানের 1 ঘণ্টায় কাজের পরিমাণ = 1/3x

তারা একসাথে 1 ঘণ্টায় যতটুকু কাজ করতে পারে = (1/x) + (1/3x) = 4/3x

একসাথে কাজটি শেষ করতে সময় লাগে = 3 ঘণ্টা

⇒ 3 ঘণ্টায় তারা পুরো ১টা কাজ শেষ করে

তাহলে,
3 × (4/3x) = 1
⇒ 4/x = 1
⇒ x = 4

সুতরাং,
আমির একা কাজটি শেষ করতে সময় নেয় = ৪ ঘণ্টা
হান্নান একা কাজটি শেষ করতে সময় নেয় = 3 × 4 = 12 ঘণ্টা

৩৪০.

A certain machine produces 1,000 units of product P per hour. Working continuously at this constant rate, this machine will produce how many units of product P in 7 days?

ক
24,000
খ
40,000
গ
7,000
ঘ
168,000

ব্যাখ্যা

Question: A certain machine produces 1,000 units of product P per hour. Working continuously at this constant rate, this machine will produce how many units of product P in 7 days?

Solution:
7 days = 7 × 24 hours = 168 hours
In 1 hour, the machine produces 1,000 units
In 168 hours, the machine produces 1,000 × 168 units = 168000 units

৩৪১.

Seven men can complete a work in 12 days. They started the work and after 5 days, two men left. In how many days will the work be completed by the remaining men?

ক
ক) 5(1/4)
খ
খ) 6(1/2)
গ
গ) 7(2/3)
ঘ
ঘ) 9(4/5)

ব্যাখ্যা

(7 × 12) men can complete the work in 1 day.
∴ 1 man's 1 day's work = 1/84.
7 men's 5 day's work = (1/12) × 5
= 5/12.
Remaining work = 1 - (5/12)
= 7/12
5 men's 1 day's work = (1/84) × 5
= 5/84.
5/84 work is done by them in 1 days.
7/12 work is done by them in (84/5) × (7/12)
= 49/5 days.
= 9(4/5) days.

৩৪২.

What is the solution of the inequality: - 6 ≤ 3x + 3 < 27?

ক
(- 3, 8)
খ
[- 3, 8]
গ
[- 3, 8)
ঘ
(- 3, 8]
ঙ
None of these

ব্যাখ্যা

Question: What is the solution of the inequality: - 6 ≤ 3x + 3 < 27?

Solution:
- 6 ≤ 3x + 3 < 27
⇒ - 6 - 3 ≤ 3x + 3 - 3 < 27 - 3
⇒ - 9 ≤ 3x < 24
⇒ - 9/3 ≤ 3x/3 < 24/3
⇒ - 3 ≤ x < 8

∴ solution of the inequality: [-3, 8)

৩৪৩.

If 8 men or 12 women can build a 240-meter road in 10 days, how many days will 6 men and 6 women take to build a 360-meter road?

ক
12 days
খ
8 days
গ
15 days
ঘ
18 days

ব্যাখ্যা

Question: If 8 men or 12 women can build a 240-meter road in 10 days, how many days will 6 men and 6 women take to build a 360-meter road?

Solution:
দেওয়া আছে, ৮ জন পুরুষের কাজের ক্ষমতা = ১২ জন মহিলার কাজের ক্ষমতা
অর্থাৎ, ২ জন পুরুষ = ৩ জন মহিলা

এখন,
৩ জন মহিলা = ২ জন পুরুষ
∴ ১ জন মহিলা = (২/৩) জন পুরুষ
∴ ৬ জন মহিলা = ৬ × (২/৩) = ৪ জন পুরুষ
সুতরাং, মোট শ্রমিক সংখ্যা = ৬ জন পুরুষ + ৪ জন পুরুষ = ১০ জন পুরুষ।

৮ জন পুরুষ ২৪০ মিটার রাস্তা তৈরি করে ১০ দিনে।
∴ ১ জন পুরুষ ২৪০ মিটার রাস্তা তৈরি করে = (১০ × ৮) = ৮০ দিনে
∴ ১ জন পুরুষ ১ মিটার রাস্তা তৈরি করে = (৮০ ÷ ২৪০) = ১/৩ দিনে
∴ ১০ জন পুরুষ ১ মিটার রাস্তা তৈরি করে = (১/৩ ÷ ১০) = ১/৩০ দিনে
∴ ১০ জন পুরুষ ৩৬০ মিটার রাস্তা তৈরি করে = (১/৩০) × ৩৬০ = ১২ দিনে।

∴ ৬ জন পুরুষ এবং ৬ জন মহিলা ৩৬০ মিটার রাস্তা তৈরি করতে ১২ দিন সময় নেবে।

৩৪৪.

In a camp of soldiers there was a stock of food for 90 days for 6000 soldiers. After 30 days, 2400 soldiers left the barracks. For how many days shall the leftover food last for the remaining soldiers?

ক
120 days
খ
100 days
গ
150 days
ঘ
160 days

ব্যাখ্যা

Question: In a camp of soldiers there was a stock of food for 90 days for 6000 soldiers. After 30 days, 2400 soldiers left the barracks. For how many days shall the leftover food last for the remaining soldiers?
Let,
the remaining food last for P days
6000 soldiers had provision for 90 days
3600 soldiers had provision for P days

ATQ,
3600/6000 = 60/P
⇒ 3/5 = 60/P
⇒ 3P = 300
⇒ P = 300/3
∴ P = 100

The remaining food last for 100 days for the remaining soldiers.

৩৪৫.

A can write 100 pages in 25 hours. A and B together can write 210 pages in 30 hours. In what time can B write 42 pages?

ক
10 hours
খ
12 hours
গ
14 hours
ঘ
18 hours
ঙ
None

ব্যাখ্যা

Question: A can write 100 pages in 25 hours. A and B together can write 210 pages in 30 hours. In what time can B write 42 pages?

Solution:
Given,
In 25 hours A can write 100 pages
∴ In 1 hour A can write 100/25 pages
= 4 pages

Here,
∴ In 1 hour A and B together can write 210/30 pages
= 7 pages
and,
B's 1 hour work = (A + B)'s 1 hour work - A's 1 hour work
= 7 - 4
= 3 pages/hour

B's time
3 pages in 1 hour
∴ 1 page in 1/3 hour
∴ 42 pages in = (1 × 42)/3 hour
= 14 hours

৩৪৬.

Anik alone can do a piece of work in 6 days and Bishal alone in 8 days. Anik and Bishal undertook to do it for Tk. 5400. With the help of Dinesh, they completed the work in 3 days. How much is to be paid to Dinesh?

ক
Tk. 675
খ
Tk. 900
গ
Tk. 870
ঘ
Tk. 780

ব্যাখ্যা

Question: Anik alone can do a piece of work in 6 days and Bishal alone in 8 days. Anik and Bishal undertook to do it for Tk. 5400. With the help of Dinesh, they completed the work in 3 days. How much is to be paid to Dinesh?

Solution:
Anik's 1day work = 1/6
Bishal's 1 day work = 1/8

∴ (Anik + Bishal + Dinesh)'s 1 day work = 1/3

∴ Dinesh's 1 day work = (1/3) - (1/6) - (1/8) = (8 - 4 - 3)/24 = 1/24

So, Dinesh's 3 day work = 3 × (1/24) = 1/8
If Dinesh contributed 8th part of work then he will receive 8th part of total payment

∴ Dinesh should be paid = 5400 × (1/8) = Tk. 675

৩৪৭.

3 pumps working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?

ক
9
খ
10
গ
11
ঘ
12

ব্যাখ্যা

Question: 3 pumps working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?

Solution:
3 pumps need 2 × 8 hours = 16 hours
1 pump needs 16 × 3 hours
4 pumps need (16 × 3)/4 hours
= 12 hours

৩৪৮.

If the workforce is doubled, how much longer will it take to finish the task?

ক
3 times
খ
2 times
গ
0.5 times
ঘ
None of these

ব্যাখ্যা

Question: If the workforce is doubled, how much longer will it take to finish the task?

Solution:
ধরি,
শ্রমিক সংখ্যা = x, এর দিগুণ = 2x,
সময় = n
x জন কাজটি করে n সময়ে

১ জন কাজটি করে = xn সময়ে
২x জন কাজটি করে = xn/২x
= n/২ সময়ে বা ১/২ সময়ে।

৩৪৯.

If 3 jackets and 5 sweaters cost Tk. 12,000, and 5 jackets and 3 sweaters cost Tk. 13,600, what is the cost of one jacket?

ক
Tk. 15000
খ
Tk. 2000
গ
Tk. 2500
ঘ
Tk. 3000

ব্যাখ্যা

Question: If 3 jackets and 5 sweaters cost Tk. 12,000, and 5 jackets and 3 sweaters cost Tk. 13,600, what is the cost of one jacket?

Solution:
ধরি, একটি জ্যাকেটের মূল্য x টাকা এবং একটি সোয়েটারের মূল্য y টাকা।

প্রশ্নমতে,
3x + 5y = 12000 ............... (i)
5x + 3y = 13600 .............. (ii)

(ii) × 5 - (i) × 3 ⇒
(25x + 15y) - (9x + 15y) = 68000 - 36000
⇒ 25x - 9x = 32000
⇒ 16x = 32000
⇒ x = 32000/16
⇒ x = 2000

সুতরাং, একটি জ্যাকেটের মূল্য 2000 টাকা।

৩৫০.

A can complete a piece of work in 18 days, B in 20 days and C in 30 days. B and C together start the work and are forced to leave after 2 days. The time taken by A alone to complete the remaining work is-

ক
20 days
খ
18 days
গ
15 days
ঘ
12 days

ব্যাখ্যা

Question: A can complete a piece of work in 18 days, B in 20 days and C in 30 days. B and C together start the work and are forced to leave after 2 days. The time taken by A alone to complete the remaining work is-

Solution:
Here,
B's 1 day's work = 1/20 part
C's 1 day's work = 1/30 part

∴ (B + C)'s 1 day's work = (1/20 + 1/30) part
∴ (B+C)'s 2 day's work = {(1/20 + 1/30) × 2} part
= [{(3+2)/60} × 2] part
= (5/60 × 2) part
= 1/6 part

Remaining work = (1 -1/6) part
= 5/6 part

A's one day's work = 1/18 part
∴ The time taken by A alone to complete the remaining work is = (5/6)/(1/18) days
= 15 days

৩৫১.

To complete a piece of work, Hasib takes 6 days and Tanveer takes 8 days alone respectively. Hasib and Tanveer took Tk.2400 to do this work. When Hamza joined them, the work was done in 3 days. What amount was paid to Hamza?

ক
ক) Tk.200
খ
খ) Tk.350
গ
গ) Tk.300
ঘ
ঘ) None of these

ব্যাখ্যা

প্রশ্ন: To complete a piece of work, Hasib takes 6 days and Tanveer takes 8 days alone respectively. Hasib and Tanveer took Tk.2400 to do this work. When Hamza joined them, the work was done in 3 days. What amount was paid to Hamza?

সমাধান:
হাসিব ১ দিনে করে ১/৬ অংশ
তানভীর ১ দিনে করে ১/৮ অংশ
হাসিব ও তানভীর একত্রে ১ দিনে করে (১/৬ + ১/৮) অংশ
= ৭/২৪ অংশ

হামজা সহ আসলে কাজ ৩ দিনে শেষ হয়।
তাহলে ৩ জনে একত্রে ১ দিনে করে ১/৩ অংশ

হামজা ১ দিনে করে ১/৩ - ৭/২৪ অংশ
= ১/২৪ অংশ

হামজা ৩ দিনে করে ৩/২৪ অংশ = ১/৮ অংশ

১ বা সম্পূর্ণ অংশের জন্য দেয়া হয় ২৪০০ টাকা
∴ ১/৮ অংশের জন্য দেয়া হয় ২৪০০/৮ টাকা
= ৩০০ টাকা

৩৫২.

A contractor employs 45 persons to do a job in 40 days. After 10 days, it was found that only one-sixth of the work was finished. How many more persons are to be employed to finish the job as per schedule?

ক
15
খ
25
গ
40
ঘ
30

ব্যাখ্যা

Question: A contractor employs 45 persons to do a job in 40 days. After 10 days, it was found that only one-sixth of the work was finished. How many more persons are to be employed to finish the job as per schedule?

Solution:
দেওয়া আছে:
মোট লোক = 45 জন
নির্ধারিত সময় = 40 দিন
10 দিনে সম্পন্ন কাজ = 1/6 অংশ

ধরি, সম্পূর্ণ কাজ = 1 একক

45 জন লোক 10 দিনে করে = 1/6 অংশ কাজ
∴ 45 জন লোক 1 দিনে করে = (1/6) ÷ 10 = 1/60 অংশ
∴ 1 জন লোক 1 দিনে করে = (1/60) ÷ 45 = 1/2700 অংশ

অবশিষ্ট কাজ = 1 - 1/6 = 5/6 অংশ
অবশিষ্ট সময় = 40 - 10 = 30 দিন

∴ অবশিষ্ট 5/6 অংশ কাজ 30 দিনে করতে হবে

∴ প্রতিদিনের প্রয়োজনীয় কাজের হার = (5/6) ÷ 30 অংশ
= 5/180 = 1/36 অংশ

এখন,
প্রতিদিন 1/2700 অংশ কাজ করে 1 জন
∴ 1 অংশ কাজ করে = 1 ÷ (1/2700) জন
∴ 1/36 অংশ কাজ করে = (2700/36) জন
= 75 জন

∴ অতিরিক্ত লোকের প্রয়োজন = 75 - 45 = 30 জন

৩৫৩.

A works twice as fast as B. If B can complete a work in 18 days independently, the number of days in which A and B can together finish the work is:

ক
ক) 4 days
খ
খ) 6 days
গ
গ) 8 days
ঘ
ঘ) 10 days
ঙ
ঙ) None of these

ব্যাখ্যা

Ratio of rates of working of A and B = 2:1.
So, ratio of times taken = 1:2
Therefore, A's 1 day's work = 1/9
B's 1 day's work = 1/18
(A + B)'s 1 day's work = 1/9 + 1/18 = 1/6
So, A and B together can finish the work in 6 days.

৩৫৪.

A can finish a job in 18 days, B in 12 days, and C in 6 days. B and C begin the work together but have to stop after working for 2 days. How many days will A alone take to complete the remaining work?

ক
9 days
খ
25 days
গ
15 days
ঘ
3 days

ব্যাখ্যা

Question: A can finish a job in 18 days, B in 12 days, and C in 6 days. B and C begin the work together but have to stop after working for 2 days. How many days will A alone take to complete the remaining work?

Solution:
Work done by B and C in 1 day:
B's 1-day work = 1/12,
C's 1-day work = 1/6
B + C in 1 day = 1/12 + 1/6
= (1 + 2)/12
= 3/12
= 1/4

Work done by B and C in 2 days = 2 × 1/4 = 1/2

Remaining work = 1 - 1/2 = 1/2

A's 1-day work = 1/18

∴ Time for A to finish remaining work = (1/2) ÷ (1/18)
= 1/2 × 18
= 9 days

৩৫৫.

Working 5 hours a day, Samiya can complete a work in 8 days and working 6 hours a day, Fahima can complete the same work in 10 days. Working 6 hours a day, they can jointly complete the work in:

ক
8 days
খ
6 days
গ
3 days
ঘ
4 days
ঙ
None

ব্যাখ্যা

Question: Working 5 hours a day, Samiya can complete a work in 8 days and working 6 hours a day, Fahima can complete the same work in 10 days. Working 6 hours a day, they can jointly complete the work in:

Solution:
Working 5 hours a day, Samiya can complete a work in 8 days = 8 × 5 = 40 hours
Working 6 hours a day, Fahima can complete a work in 10 days = 6 × 10 = 60 hours

(Samiya and Fahima)'s 1 hour's work = (1/40) + (1/60)
= (3 + 2)/120
= 5/120
= 1/24

They can jointly complete the work in 24 hours
Working 6 hours a day, they can jointly complete the work in = 24/6 = 4 days

৩৫৬.

A contract is to be completed in 46 days and 117 men were set to work, each working 8 hours a day. After 33 days (4/7) th of work is completed. How many additional men may be employed so that the work may be completed in time, each man now working 9 hours a day?

ক
51 men
খ
68 men
গ
81 men
ঘ
98 men

ব্যাখ্যা

Question: A contract is to be completed in 46 days and 117 men were set to work, each working 8 hours a day. After 33 days (4/7) th of work is completed. How many additional men may be employed so that the work may be completed in time, each man now working 9 hours a day?

Solution:
Remaining Work = (1 - 4/7) = 3/7
Remaining Time = (46 - 33) = 13 days

33 days working 8 hrs a day = 33 × 8 hrs = 264 hrs
13 days working 9 hrs a day = 13 × 9 hrs = 117 hrs

In 264 hrs to complete (4/7) the of work it requires 117 men
∴ In 117 hrs to complete (3/7) the of work it requires =

= 198 men

∴ Additional men required = 198 - 117 = 81 person.

৩৫৭.

A factory produces 300 units in 15 days with 10 machines working 8 hours a day. How many machines are needed to produce 500 units in 10 days working 6 hours a day?

ক
20 machines
খ
24 machines
গ
30 machines
ঘ
34 machines

ব্যাখ্যা

Question: A factory produces 300 units in 15 days with 10 machines working 8 hours a day. How many machines are needed to produce 500 units in 10 days working 6 hours a day?

Solution:
দৈনিক ৮ ঘণ্টা কাজ করে ১৫ দিনে ৩০০ ইউনিট বানায় ১০ টি মেশিন
দৈনিক ১ ঘণ্টা কাজ করে ১৫ দিনে ৩০০ ইউনিট বানায় ১০ × ৮ টি মেশিন
দৈনিক ১ ঘণ্টা কাজ করে ১ দিনে ৩০০ ইউনিট বানায় ১০ × ৮ × ১৫ টি মেশিন
দৈনিক ১ ঘণ্টা কাজ করে ১ দিনে ১ ইউনিট বানায় ১২০০/৩০০ টি মেশিন
দৈনিক ৬ ঘণ্টা কাজ করে ১ দিনে ১ ইউনিট বানায় ১২০০/(৩০০ × ৬) টি মেশিন
দৈনিক ৬ ঘণ্টা কাজ করে ১০ দিনে ১ ইউনিট বানায় ১২০০/(৩০০ × ৬ × ১০) টি মেশিন
দৈনিক ৬ ঘণ্টা কাজ করে ১০ দিনে ৫০০ ইউনিট বানায় (১২০০ × ৫০০)/(৩০০ × ৬ × ১০) টি মেশিন
= ৩৩.৩৩ টি মেশিন
≈ ৩৪ টি মেশিন

৩৫৮.

A takes thrice as long to do a piece of work, as B takes. A & B together can finish a piece of work in 15 days. A alone can do it in -

ক
ক) 15 days
খ
খ) 25 days
গ
গ) 45 days
ঘ
ঘ) 60 days

ব্যাখ্যা

ধরি,
B কাজটি করতে সময় নেয় = x দিন
A কাজটি করতে সময় নেয় = 3x দিন

A এবং B 1 দিনে করতে পারে কাজটির = (1/x) + (1/3x) অংশ
= (3 + 1)/3x
= 4/3x
A এবং B 4/3x অংশ কাজ করতে সময় লাগে = 1 দিন
A এবং B 1 অংশ কাজ করতে সময় লাগে = 1/(4/3x) দিন
= 3x/4

প্রশ্নমতে,
3x/4 = 15
x = (15 × 4)/3
x = 20

A কাজটি করতে সময় নেয় = 3× 20 দিন = 60 দিন

৩৫৯.

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:

ক
39
খ
42
গ
40
ঘ
50
ঙ
35

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

⇒ 125 × x = 150 × 35

⇒ x = (150 × 35)/125

= 42

৩৬০.

A can do a piece of work in 4 hours, B and C together in 3 hours, and A and C together in 2 hours. How long will B alone take to do it?

ক
ক) 8 hours
খ
খ) 12 hours
গ
গ) 10 hours
ঘ
ঘ) 24 hours

ব্যাখ্যা

Question: A can do a piece of work in 4 hours, B and C together in 3 hours, and A and C together in 2 hours. How long will B alone take to do it?

Solution:
A's 1 hour's work = 1/4
(B + C)'s 1 hour's work = 1/3
(A + C)'s 1 hour's work = 1/2

∴C's 1 hour's work = (1/2) - (1/4) = 1/4

B's 1 hour's work = (1/3) - (1/4) = 1/12

Hence, B will complete the whole work in 12 hours.

৩৬১.

A contractor undertook to finish a piece of work in 100 days and employed 75 men. After 50 days, 2/5 of the work was completed. How many additional men should be employed to complete the work on schedule?

ক
25 men
খ
38 men
গ
33 men
ঘ
43 men

ব্যাখ্যা

Question: A contractor undertook to finish a piece of work in 100 days and employed 75 men. After 50 days, 2/5 of the work was completed. How many additional men should be employed to complete the work on schedule?

Solution:
We know that 75 men completed 2/5 of the work in 50 days. Therefore, the amount of work done by 1 man in 50 days is:
Work done by 1 man in 50 days = 2/(5×75) = 2/375

Remaining work = 1 - 2/5 = 3/5

Number of men required = Remaining work / Work done by 1 man in 50 days
= (3/5)/(2/375)
= 112.5

Since the number of workers must be an integer, round up to 113 workers.

Additional workers = 113 − 75 = 38

৩৬২.

P takes twice as much time as Q or three times as much time as R to finish a piece of work. Working together, they can finish the work in 2 days. Q can do the work alone in how many days?

ক
6 days
খ
4 days
গ
8 days
ঘ
10 days

ব্যাখ্যা

Question: P takes twice as much time as Q or three times as much time as R to finish a piece of work. Working together, they can finish the work in 2 days. Q can do the work alone in how many days?

Solution:
ধরা যাক,
P, Q ও R এর যথাক্রমে কাজটি শেষ করতে সময় লাগে x, x/2, এবং x/3 দিন।

তারা একসাথে 2 দিনে কাজ শেষ করে।
অর্থাৎ তাদের একদিনের কাজ হলো 1/2 অংশ।

∴ P + Q + R এর একদিনের কাজ = (1/x) + (2/x) + (3/x)
= (1 + 2 + 3)/x
= 6/x

শর্তমতে,
6/x = 1/2
∴ x = 12

∴ Q একা কাজ শেষ করতে সময় নেবে = 12/2 = 6 দিন।

৩৬৩.

Abir does 80% of a work in 20 days. He then calls in Belal and they together finish the remaining work in 3 days. How long Belal alone would take to do the whole work?

ক
30 days
খ
55/2 days
গ
75 days
ঘ
75/2 days

ব্যাখ্যা

৩৬৪.

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 -

ক
4 days
খ
6 days
গ
8 days
ঘ
12 days

ব্যাখ্যা

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 = 12.
So, B takes 6 days to finish the work.

৩৬৫.

A plumber charges Tk. 60 as a service fee plus Tk. 25 per hour for labor. If a customer's total cost is Tk. 185, what is the maximum number of full hours the plumber can work?

ক
10 hours
খ
8 hours
গ
6 hours
ঘ
5 hours

ব্যাখ্যা

Question: A plumber charges Tk. 60 as a service fee plus Tk. 25 per hour for labor. If a customer's total cost is Tk. 185, what is the maximum number of full hours the plumber can work?

Solution:
Given that,
Fixed service fee = Tk. 60
Charge per hour = Tk. 25
Total bill = Tk. 185

Let h = number of full hours the plumber works.

Now, total cost equation,
60 + 25h ≤ 185
⇒ 25h ≤ 185 - 60
⇒ 25h ≤ 125
⇒ h ≤ 125/25
∴ h ≤ 5

So, the plumber can work a maximum of 5 full hours.

৩৬৬.

A works twice as fast as B. If B can complete a work in 12 days immediately, the number of days in which A and B can together finish the work-

ক
3 days
খ
4 days
গ
6 days
ঘ
8 days

ব্যাখ্যা

Question: A works twice as fast as B. If B can complete a work in 12 days immediately, the number of days in which A and B can together finish the work-

Solution:
B can complete a work in 12 days
So, A can complete the work in 6 days

(A + B)'s 1 days work = (1/6 + 1/12) = 1/4 part
So, (A + B) can complete the work in 4 days.

৩৬৭.

A and B can do a job together in 7 days. A is 1.75 times as efficient as B. The same job can be done by A alone in-

ক
9.33 days
খ
11 days
গ
12.25 days
ঘ
16.33 days
ঙ
None of these

ব্যাখ্যা

Question: A and B can do a job together in 7 days. A is 1.75 times as efficient as B. The same job can be done by A alone in-

Solution:
1.75 = 175/100 = 7/4
(A's 1 day's work) : (B's 1 day's work) = 7/4 : 1 = 7 : 4.
Let A's and B's 1 day's work be 7x and 4x respectively.
Then,
7x + 4x = 1/7
⇒ 11x = 1/7
⇒ x = 1/77

A's 1 day's work = (1/77) × 7 = 1/11
∴ A can do the work in 11 days.

৩৬৮.

Rakib and Sakib aimed to finish a job in 8 days. But Rakib remains ideal for 8 days then started to work and they both finished the rest of the job in 4 days. Sakib alone can do it in -

ক
ক) 8 days
খ
খ) 10 days
গ
গ) 12 days
ঘ
ঘ) 16 days

ব্যাখ্যা

Question: Rakib and Sakib aimed to finish a job in 8 days. But Rakib remains ideal for 8 days then started to work and they both finished the rest of the job in 4 days. Sakib alone can do it in -

Solution:
দুইজন ৮ দিনে করে ১ অংশ
৪ দিনে করে ১/২ অংশ।

তাহলে বাকি ১/২ কাজ সাকিব একা ৮ দিনে করে।
তাহলে সম্পূর্ণ কাজ শেষ করতে সময় লাগবে (৮ × ২) = ১৬ দিনে।

৩৬৯.

Of a pole in a pond, 0.20 portions are in mud, 0.50 of it in water and the rest 6 feet is above water. What is the length of the pole?

ক
ক) 40 feet
খ
খ) 35 feet
গ
গ) 30 feet
ঘ
ঘ) 25 feet
ঙ
ঙ) 20 feet

ব্যাখ্যা

Question: Of a pole in a pond, 0.20 portions are in mud, 0.50 of it in water and the rest 6 feet is above water. What is the length of the pole?
Solution:
Total portion in mud and water = (0.20 + 0.50) = 0.70
The portion above water = 1 - 0.70 = 0.30

length of 0.30 = 3/10 portion is 6 feet
∴ length of 1 or Total portion of pole = (6 × 10)/3 feet
= 20 feet

৩৭০.

A can complete a piece of work in 6 days working 8 hours a day, and B can complete the same work in 12 days working 8 hours a day. How long will it take them to complete the work together if they work 4 hours a day?

ক
6 days
খ
5 days
গ
10 days
ঘ
8 days

ব্যাখ্যা

Question: A can complete a piece of work in 6 days working 8 hours a day, and B can complete the same work in 12 days working 8 hours a day. How long will it take them to complete the work together if they work 4 hours a day?

Solution:
A can complete the work in 8 × 6 = 48 hours
1 hour's work of A = 1/48 part

B can complete the work in 8 × 12 = 96 hours
1 hour's work of B = 1/96 part

(A + B)'s 1 hour's work = (1/48) + (1/96) part
= (2 + 1)/96 part
= 3/96 part
= 1/32

∴ Time taken by (A + B) working 4 hours daily = 32/(1 × 4)
= 8 days

৩৭১.

If the cost of q metres of wire is Tk. k, then what is the cost of p metres of wire at the same rate (in Tk)?

ক
pq/k
খ
kp/q
গ
q/kp
ঘ
kq/p

ব্যাখ্যা

Question: If the cost of q metres of wire is Tk. k, then what is the cost of p metres of wire at the same rate (in Tk)?

Solution:
Cost of q metres = Tk. k
Cost of 1 metre = Tk. k/q
Cost of p metres = Tk. (k × p/q) = Tk. kp/q

৩৭২.

Tamim and Sakib can do a piece of work in 20 days and 12 days respectively. Tamim started the work alone and then after 4 days, Sakib joined him till the completion of the work. How long did the work last?

ক
8 days
খ
9 days
গ
10 days
ঘ
12 days

ব্যাখ্যা

Question: Tamim and Sakib can do a piece of work in 20 days and 12 days respectively. Tamim started the work alone and then after 4 days, Sakib joined him till the completion of the work. How long did the work last?

Solution:
Work done by Tamim in 4 days = (1/20) × 4 = 1/5
∴ Remaining work = 1 - (1/5) = 4/5

(Tamim + Sakib)'s 1day's work = (1/20) + (1/12)
= 8/60 = 2/15

Now, 2/15 work is done by Tamim and Sakib in 1 day.
So, 4/5 work will be done by Tamim and Sakib in = (15/2) × (4/5)
= 6 days

∴ Total time taken = (6 + 4) days = 10 days

৩৭৩.

X can do a work in 15 days, and Y in 10 days. They work together for 3 days. How much of the work is left?

ক
1/4
খ
1/2
গ
2/5
ঘ
3/4

ব্যাখ্যা

Question: X can do a work in 15 days, and Y in 10 days. They work together for 3 days. How much of the work is left?

Solution:
X, 15 দিনে করতে পারে কাজটির 1 অংশ
∴ X ,1 দিনে করতে পারে কাজটির 1/15 অংশ

Y, 10 দিনে করতে পারে কাজটির 1 অংশ
∴ Y, 1 দিনে করতে পারে কাজটির 1/10 অংশ

X ও Y 1 দিনে একত্রে করতে পারে কাজটির = {(1/15) + (1/10)} অংশ
= (2 + 3)/30 অংশ
= 5/30 অংশ
= 1/6 অংশ

X ও Y 3 দিনে করতে পারে কাজটির (3 × 1/6) অংশ
= 1/2 অংশ

কাজ বাকি থাকে = 1 - (1/2) অংশ
= (2 - 1)/2 অংশ
= 1/2 অংশ

∴ কাজটির 1/2 অংশ বাকি থাকে।

৩৭৪.

A factory has two machines, X and Y. Machine X can produce 6,000 items in 10 days, working 6 hours per day. Machine Y can produce 8,000 items in 8 days, working 10 hours per day. If both machines work together for 8 hours per day, how many days will they take to produce 24,000 items?

ক
10 days
খ
12 days
গ
15 days
ঘ
18 days

ব্যাখ্যা

Question: A factory has two machines, X and Y. Machine X can produce 6,000 items in 10 days, working 6 hours per day. Machine Y can produce 8,000 items in 8 days, working 10 hours per day. If both machines work together for 8 hours per day, how many days will they take to produce 24,000 items?

Solution:
Total hours worked by Machine X = 10 days × 6 hours/day = 60 hours.
Rate of X = (6000/60) = 100 items/hour

Total hours worked by Machine Y = 8 days × 10 hours/day = 80 hours.
Rate of Y = (8000/80) = 100 items/hour

Combined rate = Rate of X + Rate of Y = 100 + 100 = 200 items/hour.

So, time required = {24000/(200 × 8)} = 15 days.

৩৭৫.

A takes twice as long to do a piece of work, as B takes. A & B together can finish a piece of work in 20 days. A alone can do it in-

ক
ক) 25 days
খ
খ) 30 days
গ
গ) 35 days
ঘ
ঘ) 60 days

ব্যাখ্যা

ধরি,
B কাজটি করতে সময় নেয় = x দিন
A কাজটি করতে সময় নেয় = 2x দিন

A এবং B 1 দিনে করতে পারে কাজটির = (1/x) + (1/2x) অংশ
= (2 + 1)/2x
= 3/2x
A এবং B 3/2x অংশ কাজ করতে সময় লাগে = 1 দিন
A এবং B 1 অংশ কাজ করতে সময় লাগে = 1/(3/2x) দিন
= 2x/3

প্রশ্নমতে,
2x/3 = 20
x = (20 × 3)/2
x = 30

A কাজটি করতে সময় নেয় = 2 × 30 দিন = 60 দিন

৩৭৬.

While working 9 hour a day, A alone can complete a piece of work in 5 days and B alone in 10 days. In what time would they complete it together, 6 hour a day?

ক
4 days
খ
5 days
গ
6 days
ঘ
7 days

ব্যাখ্যা

Question: While working 9 hour a day, A alone can complete a piece of work in 5 days and B alone in 10 days. In what time would they complete it together, 6 hour a day?

Solution:
A can complete the work in 9 × 5 = 45 hours
1 hour's work of A = 1/45 part

B can complete the work in 9 × 10 = 90 hours
1 hour's work of B = 1/90 part

(A + B)'s 1 hour's work = (1/45) + (1/90) part
= (2 + 1)/90 part
= 3/90 part
= 1/30

∴ Time taken by (A + B) working 6 hours daily = 30/(1 × 6)
= 5 days

৩৭৭.

X can do a piece of work in 40 days. He works at it for 8 days and then Y finished it in 16 days. How long will they together take to complete the work?

ক
13.33 days
খ
15 days
গ
20.25 days
ঘ
26.67 days

ব্যাখ্যা

Question: X can do a piece of work in 40 days. He works at it for 8 days and then Y finished it in 16 days. How long will they together take to complete the work?

Solution:
Work done by X in 8 days = (1/40) × 8 = 1/5

Remaining work = 1 - (1/5) = 4/5

Now,
4/5 work is done by Y in 16 days
Whole work will be done by Y in = (16 × 5)/4
= 20 days

∴ X's 1 day's work = 1/40
∴ Y's 1 day's work = 1/20

(X + Y)'s 1 day's work
= 1/40 + 1/20
= 3/40

Hence, X and Y will together complete the work in
= 40/3 = 13.33 days

৩৭৮.

The speed of a car increases by 2 kms after every one hours. If the distance travelled in the first one hour was 35 kms, what was the total distance travelled in 12 hours?

ক
602 kms.
খ
586 kms.
গ
570 kms.
ঘ
552 kms.

ব্যাখ্যা

Question: The speed of a car increases by 2 kms after every one hours. If the distance travelled in the first one hour was 35 kms, what was the total distance travelled in 12 hours?

Solution:
Total distance travelled in 12 hours = (35 + 37 + 39 +..... upto 12 terms)
This is an A.P with first term, a = 35 ,
number of terms, n = 12
d = 2

Required distance = (12/2){(2 × 35) + (12 - 1) × 2}
= 6 × (70 + 22)
= 552 kms.

৩৭৯.

If 12 men and 16 boys can do apiece of work in 5 days; 13 men and 24 boys can do it in 4 days, then the ratio of the daily work done by a man to that of a boy is -

ক
ক) 2:1
খ
খ) 3:1
গ
গ) 3:2
ঘ
ঘ) 5:4

ব্যাখ্যা

Let, 1 man's 1 day's work = x and
1 boy's 1 day's work = y

Then, 12x + 16y = 1/5
and 13x + 24y = 1/4.

Solving these two equations, we get,
x = 1/100 and
y = 1/200
∴ Required ratio = x : y
= 1/100 : 1/200
= 2 : 1.

৩৮০.

A cistern can be filled by two pipes P & Q in 20 and 30 min respectively. Both pipes being open, when must the first pipe be turned off so that the cistern may be filled in 10 minutes more?

ক
8 minutes
খ
6 minutes
গ
5 minutes
ঘ
4 minutes

ব্যাখ্যা

Question: A cistern can be filled by two pipes P & Q in 20 and 30 min respectively. Both pipes being open, when must the first pipe be turned off so that the cistern may be filled in 10 minutes more?

Solution:
In 1 min both pipes can fill = (1/20) + (1/30)
= (3 + 2)/60
= 5/60 = 1/12
In 10 min second pipe can fill = (1/30) × 10 = 1/3 part

Part of cistern filled by both the pipes = 1 - 1/3
= (3 - 1)/3 = 2/3

1/12 part is filled in 1 min
∴ 2/3 part will be filled in (12 × 2)/3 = 8 min
Hence, the first pipe should be turned off after 8 min.

৩৮১.

The regular hourly wage for an employee of a certain factory is $5.60. If the employee worked 8 hours overtime and earned 3/2 times this regular hourly wage for overtime, how much overtime money was earned?

ক
$ 67.20
খ
$ 55.40
গ
$ 50.00
ঘ
$ 44.80

ব্যাখ্যা

Question: The regular hourly wage for an employee of a certain factory is $ 5.60. If the employee worked 8 hours overtime and earned 3/2 times this regular hourly wage for overtime, how much overtime money was earned?

Solution:
Regular wage = $ 5.6
Overtime wage = (3/2) × 5.6 = $ 8.4
For 8 hour overtime, money = 8.4 × 8 = 67.2

৩৮২.

A and B can complete a piece of work in 18 days and 12 days respectively. They got a contract to complete the work for TK. 60000. The share of A in the contracted money will be-

ক
36000 Taka
খ
24000 Taka
গ
20000 Taka
ঘ
22000 Taka

ব্যাখ্যা

Question: A and B can complete a piece of work in 18 days and 12 days respectively. They got a contract to complete the work for TK. 60000. The share of A in the contracted money will be-

Solution:
Ratio of number of days taken by A and B to complete the work = 18 : 12 = 3 : 2
∴ Ratio of efficiency of A and B = 2 : 3

Let their shares is in the ratio of 2x and 3x
Now,
2x + 3x = 60000
or, 5x = 60000
∴ x = 60000/5 = 12000

∴ share of A = 2x = 2 × 12000 = 24000 Taka

৩৮৩.

A parking garage rents parking spaces for Tk. 10 per week or Tk. 30 per month. How much does a person save in a year by renting by the month rather than by the week?

ক
Tk. 140
খ
Tk. 160
গ
Tk. 220
ঘ
Tk. 240

ব্যাখ্যা

Question: A parking garage rents parking spaces for Tk. 10 per week or Tk. 30 per month. How much does a person save in a year by renting by the month rather than by the week?

Solution:

Tk. 10 per week

An year has 52 weeks.

Annual charges per year at Tk. 10 per week = 52 × 10 = 520

Tk. 30 per month

An year has 12 months.

Annual charges per year at Tk. 30 per month = 12 × 30 = 360

∴ Save = 520 - 360 = 160

৩৮৪.

Half of a cistern is filled by pipe A in 4 hours whereas drained by pipe B in 5 hours. How much time will it take to fill the cistern if both the pipes are opened?

ক
30 hours
খ
20 hours
গ
40 hours
ঘ
32 hours

ব্যাখ্যা

Question: Half of a cistern is filled by pipe A in 4 hours whereas drained by pipe B in 5 hours. How much time will it take to fill the cistern if both the pipes are opened?

Solution:
A can fill the cistern in 8 hours
B can drain it in 10 hours

together they can fill = 1/8 - 1/10
= 1/40

∴ total time to fill the cistern is 40 hours.

৩৮৫.

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?

ক
4 days
খ
3 days
গ
2 days
ঘ
5 days

ব্যাখ্যা

Question: 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?

Solution:
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 = 24 hour

∴ as the will work 8 hour a day, it will take = 24/8 = 3 days

৩৮৬.

Hadi takes twice as much as Mahbub or thrice as much time as Rana to finish a piece of work. Working together, they can finish the work in 3 days. Hadi can do the work alone in-

ক
ক) 6 days
খ
খ) 12 days
গ
গ) 16 days
ঘ
ঘ) 18 days

ব্যাখ্যা

Question: Hadi takes twice as much as Mahbub or thrice as much time as Rana to finish a piece of work. Working together, they can finish the work in 3 days. Hadi can do the work alone in -

Solution:
Let, Hadi, Mahbub, and Rana take 6x, 6x/2 = 3x, and 6x/3 = 2x respectively.

Now,
(1/6x) + (1/3x) + (1/2x) = 1/3
⇒ 6/6x = 1/3
⇒ 1/x = 1/3
⇒ x = 3

So, Hadi takes = 6 × 3 = 18 days

৩৮৭.

'A' can do a work in 10 days, and 'B' in 15 days. They work together for 4 days. How much of the work is left?

ক
1/3
খ
1/4
গ
1/2
ঘ
3/8

ব্যাখ্যা

Question: 'A' can do a work in 10 days, and 'B' in 15 days. They work together for 4 days. How much of the work is left?

Solution:
মনে করি,
সম্পূর্ণ কাজ = 1 অংশ

∴ A একা একদিনে করে = 1/10 অংশ।
B একা একদিনে করে = 1/15 অংশ।

∴ A ও B একসাথে একদিনে করে = (1/10) + (1/15) অংশ
= (3 + 2)/30
= 5/30
= 1/6 অংশ

∴ A ও B একসাথে 4 দিনে করে = 4 × (1/6) অংশ
= 2/3 অংশ

∴ কাজ বাকি থাকে = 1 - (2/3) অংশ
= (3 - 2)/3
= 1/3 অংশ

৩৮৮.

12 persons can do a work in 8 days by working 5 hours a day. Working how many hours per day can 16 persons finish the work in 3 days?

ক
10 hours a day
খ
12 hours a day
গ
8 hours a day
ঘ
5 hours a day

ব্যাখ্যা

Question: 12 persons can do a work in 8 days by working 5 hours a day. Working how many hours per day can 16 persons finish the work in 3 days?

Solution:
12 persons can do a work in 8 day's by working 5 hours a day
∴ 1 person can do a work in 1 day's by working (5 × 12 × 8) hours a day
∴ 16 persons can do a work in 3 day's by working (5 × 12 ×8)/(16 × 3) hours a day
= 10 hours a day

৩৮৯.

A manager has Tk. 6000 budgeted for raises for 4 full-time and 2 part-time employees. Each of the full-time employees receives the same raise, which is twice the raise that each of the part-time employees receives. What is the amount of the raise that each full-time employee receives?

ক
Tk. 750
খ
Tk. 1000
গ
Tk. 1200
ঘ
Tk. 1500
ঙ
Tk. 1650

ব্যাখ্যা

Question: A manager has Tk. 6000 budgeted for raises for 4 full-time and 2 part-time employees. Each of the full-time employees receives the same raise, which is twice the raise that each of the part-time employees receives. What is the amount of the raise that each full-time employee receives?

Solution:
This is a simple equations problem
Let each part time employee receive a raise of Tk. y
Then each full time employee receives a raise of Tk. 2y
There are 4 full- time employees and 2 part- time employees
The total budget is Tk. 6000

So, the equation is
4(2y) + 2y = 6000
⇒ 10y = 6000
∴ y = 600

Raise for each full-time employee = 2y = 2 × 600 = Tk. 1200

৩৯০.

If 8 people make 48 chairs in 12 days by working 6 hours a day, then how long will it take 12 people working 8 hours a day to make 192 chairs?

ক
6 days
খ
12 days
গ
24 days
ঘ
30 days

ব্যাখ্যা

Question: If 8 people make 48 chairs in 12 days by working 6 hours a day, then how long will it take 12 people working 8 hours a day to make 192 chairs?

Solution:
48 টি চেয়ার তৈরি করতে 8 জন লোক প্রতিদিন 6 ঘণ্টা কাজ করে = 12 দিনে
∴ 1 টি চেয়ার তৈরি করতে 1 জন লোক প্রতিদিন 1 ঘণ্টা কাজ করে = (8 × 6 × 12)/48 দিনে
∴ 192 টি চেয়ার তৈরি করতে 12 জন লোক প্রতিদিন 8 ঘণ্টা কাজ করে = (576 × 192)/(48 × 8 × 12)
= 24 দিনে

৩৯১.

A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is -

ক
ক) 8/15
খ
খ) 7/15
গ
গ) 3/19
ঘ
ঘ) 7/25

ব্যাখ্যা

Question: A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is -

Solution:
একদিনে,
A করে 1/15 অংশ
B করে 1/20 অংশ

মোট করে = 1/15 + 1/20
= 7/60

চারদিনে মোট কাজ করে = 4 × 7/60 = 28/60 = 7/15

∴ অবশিষ্ট কাজ = 1 - 7/15 = 8/15

৩৯২.

3 pumps, working 8 hours a day, can empty a tank in 2 days, How many hours a day must 4 pumps work to empty the tank in 1 day?

ক
9 hours
খ
10 hours
গ
11 hours
ঘ
12 hours

ব্যাখ্যা

Question: 3 pumps, working 8 hours a day, can empty a tank in 2 days, How many hours a day must 4 pumps work to empty the tank in 1 day?

Solution:
3 pumps, working 8 hours a day, can empty a tank in 2 days
Formula used: M1 × T1 = M2 × T2
Where M1 and M2 is men and T1 and T2 is time

Calculation:
Let H hours be the number of hours required Applying the above formula
⇒ 3 × 8 × 2 = 4 × 1 × H
⇒ H = 48/4
⇒ H = 12 hours

∴ 4 pump need to work 12 hours to complete the work in 1 day.

৩৯৩.

A man's regular pay is Tk. 30 per hour up to 40 hours, Overtime is twice the regular payment. If he was paid Tk. 1,680, how many hours overtime did he work?

ক
ক) 7
খ
খ) 16
গ
গ) 9
ঘ
ঘ) 8

ব্যাখ্যা

ধরি,
Overtime করেছিল x ঘণ্টা

প্রশ্নমতে,
(30 × 40) + (30 × 2 × x ) = 1,680
⇒ 1,200 + 60x = 1,680
⇒ 60x = 1,680 - 1,200
⇒ 60x = 480
⇒ x = 480/60
x = 8

অতএব
সে ৪ ঘন্টা Overtime করেছিল।

৩৯৪.

To finish a work, A sets aside half additional time than B. In the event that together they take 18 days to finish the work, what amount of time might B take to do it?

ক
ক) 30 days
খ
খ) 35 days
গ
গ) 40 days
ঘ
ঘ) 45 days

ব্যাখ্যা

Suppose B takes x days. Then,
A takes 150x/100 days, i.e. 3x/2 days
∴1/x+ 2/3x= 1/18 ⇒5/3x= 1/18 ⇒3x = 90 ⇒x= 30
Hence B takes 30 days.

৩৯৫.

If 8 workers can assemble a car in 9 hours, how long would it take 12 workers to assemble the same car?

ক
3 hours
খ
6 hours
গ
9 hours
ঘ
12 hours

ব্যাখ্যা

Question: If 8 workers can assemble a car in 9 hours, how long would it take 12 workers to assemble the same car?

Solution:

Here, M₁ = 8, M₂ = 12, W₁ = W₂ = 1, T₁ = 9, T₂ = ?

(M₁ × T₁)/(M₂ × T₂) = W₁/W₂
⇒ (8 × 9)/ (12 × T₂) = 1
⇒ 12 × T₂ = 72
⇒ T₂ = 72/12
∴ T₂ = 6

৩৯৬.

A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days, B had to leave and A alone completed the remaining work. The whole work was completed in:

ক
10 days
খ
12 days
গ
14 days
ঘ
16 days

ব্যাখ্যা

Question: A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days, B had to leave and A alone completed the remaining work. The whole work was completed in:

Solution:
Work done by (A + B) in 1 day
= (1/15) + (1/10)
= (2 + 3)/30
= 5/30
= 1/6

(A + B)’s 2 days’ work = 2/6
= 1/3

∴ Remaining work = 1 - (1/3)
= 2/3

This part is done by A alone.
Since, one work is done by A in 15 days.
2/3 work is done in = 15 × (2/3)
= 10 days

So, Total number of days = (10 + 2) 12 days
= 12 days

৩৯৭.

A can complete a work in 20 days, B in 30 days, and C in 60 days. A stops working 4 days before the completion of the work, and B stops 6 days before completion. C continues working alone till the end. What was the total number of days taken to complete the entire work?

ক
10 days
খ
14 days
গ
18 days
ঘ
21 days

ব্যাখ্যা

Question: A can complete a work in 20 days, B in 30 days, and C in 60 days. A stops working 4 days before the completion of the work, and B stops 6 days before completion. C continues working alone till the end. What was the total number of days taken to complete the entire work?

Solution:
Let the total work be completed in y days.

∴ A worked for (y - 4) days
So his contribution = (y - 4)/20

B worked for (y - 6) days
So his contribution = (y - 6)/30

C worked full y days, so his contribution = y/60

Therefore,
(y - 4)/20 + (y - 6)/30 + y/60 = 1
⇒ 3(y - 4) + 2(y - 6) + y = 60
⇒ 3y - 12 + 2y - 12 + y = 60
⇒ 6y - 24 = 60
⇒ 6y = 84
⇒ y = 14

∴ The total work was completed in 14 days.

৩৯৮.

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:

ক
ক) 6 days
খ
খ) 8 days
গ
গ) 12 days
ঘ
ঘ) 4 days

ব্যাখ্যা

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 = 12.
So, B takes 6 days to finish the work.

৩৯৯.

30 men working 8 hours per day can dig a pond in 16 days. By working how many hours per day can 32 men dig the same pond, in 20 days?

ক
5 hours/day
খ
6 hours/day
গ
7 hours/day
ঘ
8 hours/day
ঙ
None

ব্যাখ্যা

Question: 30 men working 8 hours per day can dig a pond in 16 days. By working how many hours per day can 32 men dig the same pond, in 20 days?

Solution:
30 men can dig a pond in 16 days by working 8 hours per day
∴ 1 men can dig a pond in 1 days by working (8 × 30 × 16) hours per day
∴ 32 men can dig a pond in 20 days by working (8 × 30 × 16)/(20 × 32) hours per day
= 6 hours per day

৪০০.

আবির একটি নির্দিষ্ট কাজ সম্পন্ন করার জন্য বাবুলের দ্বিগুণ বা কবিরের তিনগুন সময় নেয়। তারা একত্রে ২ দিন কাজ করলে কাজটি শেষ করতে পারে। তাহলে বাবুল কতদিনে কাজটি করতে পারে?

ক
৪ দিন
খ
৬ দিন
গ
৮ দিন
ঘ
১০ দিন
ঙ
কোনটিই নয়

ব্যাখ্যা

প্রশ্ন: আবির একটি নির্দিষ্ট কাজ সম্পন্ন করার জন্য বাবুলের দ্বিগুণ বা কবিরের তিনগুন সময় নেয়। তারা একত্রে ২ দিন কাজ করলে কাজটি শেষ করতে পারে। তাহলে বাবুল কতদিনে কাজটি করতে পারে?

সমাধান:
ধরি,
আবির সময় নেয় = ক দিন
বাবলু সময় নেয় = ক/২ দিন
কবির সময় নেয় = ক/৩ দিন

প্রশ্নমতে,
(১/ক) + (২/ক) + (৩/ক) = ১/২
⇒ (১ + ২ + ৩)/ক = ১/২
⇒ ৬/ক = ১/২
⇒ ক = ১২

∴ কাজটি শেষ করতে বাবলু সময় নেয় = ১২/২ = ৬ দিন