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ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

পরীক্ষাব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্সতারিখতারিখ অনির্ধারিতসময়30 minutes
মোট প্রশ্ন২৫
সিলেবাস
Math - 05: Time & Work, Chain Rule
প্রশ্ন দেখুনঅনুশীলন
ঘনত্ব
উত্তর
উত্তরিতবর্তমানপুনরায় দেখুনঅসম্পূর্ণ

ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স · তারিখ অনির্ধারিত · ২৫ প্রশ্ন

১.
A, B and C completed a work costing Tk. 1800. A worked for 6 days, B for 4 days and C for 9 days. If their daily wages are in the ratio of 5 : 6 : 4, how much amount will be received by C?
  1. ক
    ক) Tk. 720
  2. খ
    খ) Tk. 480
  3. গ
    গ) Tk. 600
  4. ঘ
    ঘ) Tk. 820
ব্যাখ্যা
Let the daily wages of A, B and C be Tk. 5x, Tk. 6x and Tk. 4x respectively.
Then, ratio of their amounts
= (5 × 6) : (6 × 4) : (4 × 9)
= 30 : 24 : 36
= 5 : 4 : 6
∴ C's amount
= Tk. (1800 × 6/15)
= Tk. 720
২.
Fourteen persons can do a work in 18 days. After 5 days of work, 6 workers left the work, and joined back on the last day of the work. In how many days the work got completed?
  1. ক
    ক) 23
  2. খ
    খ) 27
  3. গ
    গ) 25
  4. ঘ
    ঘ) 26
ব্যাখ্যা
14 persons can do a work in 18 days
After 5 days 6 workers left.
These 5 workers joined on the last day of work.

Concept used:
If each person can do 1unit of work per day then n persons can do 1 × n unit work per day.

Calculation:
Let each person can do 1 unit of work per day

So,
⇒ 14 persons can do = 1 × 14 = 14 units/day
⇒ In 18 days, 14 persons can do = 18 × 14 = 252 units (Total work to be done)

Now,
In first 5 days, 14 persons completed
⇒ 14 × 1 × 5 = 70 units
In last day, 14 persons competed
⇒ 14 × 1 = 14 units

Then,
the total work completed in 6 days = 84 units

Now,
Work left  =168 units
And persons left = 14 - 6 = 8 persons

So,
Time taken by 8 persons to complete to leftover work
⇒ 168/(8 × 1) = 21 days

So,
time taken to complete the whole work = 5 + 21 + 1 = 27 days

∴ The work got completed in 27 days.
৩.
A can type 10 pages in 5 minutes. B can type 5 pages in 10 minutes. Working together, how many pages can they type in 30 minutes?
  1. ক
    ক) 78
  2. খ
    খ) 73
  3. গ
    গ) 75
  4. ঘ
    ঘ) 76
ব্যাখ্যা
A can type 10 pages in 5 minutes.
B can type 5 pages in 10 minutes.

Concept Used:
Total Work = Time × Efficiency

Calculation:
A can type 10 pages in 5 minutes.
A can type 1 minute = 10/5 = 2

B can type 5 pages in 10 minutes.
B can type 1 minute = 5/10 = 1/2

Both (A + B)'s type in 1 minutes = 2 + 1/2 = 5/2

The number of pages in 30 minutes = 30 × 5/2 = 75
∴ The number of pages in 30 minutes by both (A + B) is 75.
৪.
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
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
৫.
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) 28 men
  2. খ
    খ) 30 men
  3. গ
    গ) 38 men
  4. ঘ
    ঘ) 32 men
ব্যাখ্যা
Given time = 6 days 
Total men = 30
let the extra men be x So,
     30 × 4 = (30 + x) 2
=> 120 = 60 + 2x
=> 2x = 60
So, x = 30 men
৬.
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?
  1. ক
    ক) 96 days
  2. খ
    খ) 90 days
  3. গ
    গ) 98 days
  4. 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
৭.
A group of men can do a job in 25 days. But 10 men did not turn up for the job and the remaining men did the job in 30 days. The original number of men in group was
  1. ক
    ক) 40
  2. খ
    খ) 60
  3. গ
    গ) 50
  4. ঘ
    ঘ) 70
ব্যাখ্যা
The group of men can do a job = 25 Days

Formula used:

W = E × T     Where, W = Work, E = Efficiency, and T = Time

Calculation:
Let the initially the number of men be X

According to the question
⇒ 25 × X = 30 × (X - 10)
⇒ 25X = 30X - 300
⇒ 30X - 25X = 300
⇒ 5X = 300
⇒ X = 300/5 
⇒ X= 60

The initially the number of men = 60

∴ The required result will be 60.
৮.
Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?
  1. ক
    ক) 5 : 2
  2. খ
    খ) 4 : 3
  3. গ
    গ) 2 : 3
  4. ঘ
    ঘ) 3 : 2
ব্যাখ্যা
(20 × 16) women can complete the work in 1 day
1 woman's 1day's work = 1/ 320
(16 × 15) men can complete the work in 1 day
1 man's 1day's work = 1/240
So, required ratio = 1/240 : 1/320
= 1/3 : 1/4
= 4:3
৯.
If 6 spiders make 6 webs in 6 days, then one spider will make one web in how many days?
  1. ক
    ক) 9
  2. খ
    খ) 7
  3. গ
    গ) 8
  4. ঘ
    ঘ) 6
ব্যাখ্যা
Number of Spider M1 = 6
Number of days D1 = 6
Number of web W1 = 6

Number of Spider M2 = 1
Number of days D2 = ?
Number of web W2 = 1

Therefore,
(M1 × D1)/W1 = (M2 × D2)/W2
(6 × 6)/6 = (1 × D2)/1
D2 = 6

Number of days D2 = 6
১০.
A can do a piece of work in certain number of days. While B takes three days more than A to complete the same work. Working together, A and B can complete the work in two days. How many days does B take to complete the work?
  1. ক
    ক) 4
  2. খ
    খ) 6
  3. গ
    গ) 7
  4. ঘ
    ঘ) 8
ব্যাখ্যা
Let, A alone can complete the whole work in x days, then
Hence, B alone can complete the whole work in = (x + 3) days

According to the question
⇒ 1/x + 1/(x + 3) = 1/2
⇒ (x + 3 + x)/x(x + 3) = 1/2
⇒ (2x + 3)/(x2 + 3x) = 1/2
⇒ 4x + 6 = x2 + 3x
⇒ x2 - x - 6 = 0
⇒ x2 - 3x - 2x - 6 = 0
⇒ x (x - 3) + 2 (x - 3) = 0
⇒ (x - 3) (x + 2) = 0

Taking,
x - 3 = 0  (x can’t be -2)
x = 3

Hence, x + 3 = 3 + 3 = 6
∴ B alone can complete the whole work in 6 days.

Short Trick:
Let, B alone can compete the whole work in 6 days
A alone can complete the whole work in = 6 - 3 = 3 days

Total work = 6
A and B together can complete the whole work in = 6/(2 + 1) = 2 days (satisfied)

So, we can say B alone can complete the whole work in 6 days.
১১.
X can do a piece of work in 20 days and Y can do the 1/7th of the same work in 5 days. In how many days together can they complete the 11/20th of the total work?
  1. ক
    ক) 7 days
  2. খ
    খ) 14 days
  3. গ
    গ) 10 days
  4. ঘ
    ঘ) 12 days
ব্যাখ্যা
X can do in 1 day = 1/20 part 
Y can do in 1 day = 1/(7×5) = 1/35 part
X & Y together can do in 1 day = 1/20 + 1/35 = 11/140
11/140 part of the work is done in 1 day
So, 11/20 part of the work is done in = (11/20) × (140/11) = 7 days
১২.
A and B undertook to do a piece of work for Tk. 4,500. A alone could do it in 8 days and B alone in 12 days. With the assistance of C they finished the work in 4 days. Then C’s share of money is -
  1. ক
    ক) Tk. 950
  2. খ
    খ) Tk. 850
  3. গ
    গ) Tk. 750
  4. ঘ
    ঘ) Tk. 650
ব্যাখ্যা
Time taken by A to do the work = 8 days
Time taken by B to do the work = 12 days
Time taken by A, B and C together to do the work = 4 days

Calculation:
Let the total work be LCM (8, 12, 4).

LCM (8, 12, 4) = 24 unit

In one day A do = 24/8 unit
⇒ 3 unit

In one day B do = 24/12 unit
⇒ 2 unit

In one day A, B and C do = 24/4 unit
⇒ 6 unit

In one day only C do = 6 - (3 + 2)
⇒ 1 unit

The proportion of their shares = A's 1-day work : B's 1-day work : C's 1-day work
⇒ 3 : 2 : 1

According to the question,
Total share = 4500
⇒ 6 unit = 4500
⇒ 1 unit = 750

So, C's share  = Tk. 750

∴ The C’s share of the money is Tk. 750.
১৩.
A does double the work of B in the same time. If they work together, they can dig a canal in 16 days. How many days would B take if he had to dig the same canal working alone?
  1. ক
    ক) 36 days
  2. খ
    খ) 24 days
  3. গ
    গ) 18 days
  4. ঘ
    ঘ) 48 days
ব্যাখ্যা
A does double the work of B in the same time

Number of days to dig canal = 16 days

Formula used:
Efficiency = Work done/Time


According to the question
The ratio of efficiency of A to B = 2 ∶ 1
Total work = (2 + 1) × 16 = 48

Number of days B alone takes to dig the canal = 48/1
⇒ 48 days

∴ The number of days B alone takes to dig the canal is 48 days.
১৪.
A can do a piece of work in 42 days and B is thrice as efficient as A. If B joins A on 22nd day then in how many days will the work be completed?
  1. ক
    ক) 5.75
  2. খ
    খ) 5.25
  3. গ
    গ) 5.35
  4. ঘ
    ঘ) 5.45
ব্যাখ্যা
A alone can complete the work = 42 days

Formula used:
W = E × T     
Where, W = The work, E = The efficiency, and T = The time

Let us assume the work will be completed in X days
⇒ The one day work of A = 1/42
⇒ The one day work of B = 3 × (1/42) = 1/14
⇒ The 21 days work of A = 21 × (1/42) = 1/2
⇒ The remaining work = 1 - 1/2 = 1/2
⇒ The efficiency of A and B together = (1/42 + 1/14) = 4/42 = 2/21
⇒ The remaining work will be completed = (1/2) × (21/2) = 21/4 = 5.25 days

∴ The required result will be 5.25 days.
১৫.
A and B undertake to do a piece of work for Tk. 18,750. A can do it in 20 days and B can do it in 30 days. With the help of C, they finished it in 8 days. How much C should be paid for his work in proportion?
  1. ক
    ক) Tk. 6,050
  2. খ
    খ) Tk. 6,250
  3. গ
    গ) Tk. 6,750
  4. ঘ
    ঘ) Tk. 6,850
ব্যাখ্যা
A and B undertake to do a piece of work for Rs. 18,750

A can do it in 20 days and B can do it in 30 days.

Concept used:
Total work = LCM of the time taken by workers alone
Share of the amount is in the ratio of efficiency

Calculation:
LCM of 20 and 30 is 60 i.e total work
So, efficiency of A and B is 60/20 = 3, 60/30 = 2
Efficiency of A + B + C = 60/8 = 7.5
Efficiency of C = 7.5 - 3 - 2 = 2.5

Share of C = (18750/7.5) × 2.5
⇒ 18750/3
⇒ 6250

∴ C should be paid Tk. 6250 for his work in proportion

১৬.
A man completes 5/8 of a job in 10 days. At this rate, how many more days will it take him to finish the job?
  1. ক
    ক) 4
  2. খ
    খ) 3
  3. গ
    গ) 6
  4. ঘ
    ঘ) 2
ব্যাখ্যা
Work done = 5/8
Balance work =(1 - 5/8) = 3/8
Let the required number of days be x.
Then,(5/8 : 3/8) :: 10 : x
⇒ 5/8 × x = 3/8 × 10
⇒ x = 3/8 × 10 × 8/5
⇒ x = 6.
১৭.
If seven persons can build a house in 30 days, how long will it take three persons to build the same house, provided that they all work at the same rate?
  1. ক
    ক) 90 days
  2. খ
    খ) 80 days
  3. গ
    গ) 70 days
  4. ঘ
    ঘ) 85 days
ব্যাখ্যা
Seven persons can build a house = 30 days

Formula Used:
Total work = Number of people × Number of days

Calculation: 
Total Work = 30 × 7 = 210 units
⇒ Number of days = 210/3 = 70 days

∴ 70 days they all work at the same rate.

The correct option is 2 i.e. 70 days  
১৮.
A can do a certain work in 15 days. B is 25% more efficient than A. Both worked together for 4 days. C alone completed the remaining work in 8 days. A, B and C together will complete the same work in ?
  1. ক
    ক) 7 days
  2. খ
    খ) 5 days
  3. গ
    গ) 8 days
  4. ঘ
    ঘ) 9 days
ব্যাখ্যা
Work done by A = 15 days
B is 25% more efficient than A
A and B worked together = 4 days
C alone completed the remaining work = 8 days

Formula used:
Work done = Time × Efficiency

B is 25% more efficient than A
⇒ (15 × 100/125) 
⇒ 12 days

B can do the work on 12 days

Now,
LCM of 15 and 12 is 60

A's 1 day work = 4 units
B's 1 day work = 5 units

Work done by A and B work together for 4 days = (4 + 5) × 4 = 36 work

 Work left  = 60 – 36 = 24 units

C can do the remaining work = 24/8 units = 3 units

Now, A, B and C completed the whole work = 60/(4 + 5 + 3)

⇒ 60/12 days

⇒ 5 days

∴ A, B, and C completed the same work together in 5 days
১৯.
Titu, Pintu and Mithu can complete a piece of work in 18, 6 and 12 days respectively. Working together, they will complete the same work in:
  1. ক
    ক) 36/5 days 
  2. খ
    খ) 36/7 days 
  3. গ
    গ) 36/13 days 
  4. ঘ
    ঘ) 36/11 days
ব্যাখ্যা
(Titu + Pintu + Mithu)'s 1 day's work =(1/18) + (1/6) + (1/12)
                                                           =(2 + 6 + 3)/36
                                                           = 11/36

All the three together will complete the job in 36/11 days
২০.
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
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
২১.
If 4/9th of a bucket is filled in 1 minute, the rest of it will be filled in?
  1. ক
    ক) 0.75 minute
  2. খ
    খ) 1.5 minute
  3. গ
    গ) 1.25 minute
  4. ঘ
    ঘ) 1.95 minute
ব্যাখ্যা
Remaining part = 1- (4/9) = 5/9

Let the required time be x minutes
More volume to be filled, More time taken (Direct proportion)

∴ 4/9:5/9::1:x
⇒ (4/9)x = 5/9
⇒ x = (5/9)×(9/4)
⇒ x = 5/4
⇒ x = 1.25
 
২২.
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
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

২৩.
41 girls can complete a piece of work in 40 days. If x girls started the work and after 30 days 64 more girls joined them so that the whole work gets finished in the desired time, find the value of x.
  1. ক
    ক) 21
  2. খ
    খ) 25
  3. গ
    গ) 23
  4. ঘ
    ঘ) 27
ব্যাখ্যা
41 girls can complete a piece of work in 40 days.
x girls started the work 
And after 30 days 64 more girls joined them

Concept Used:
Total work = Efficiency × Time 
Here, we will take Efficiency = Number of workers
i.e Total work = Number of workers × Time 

Calculation:
Total work = 41 × 40 = 1640 units

According to the question

For the second case 
Total work = (x × 30) + (x + 64) × 10

So, we can write 
(x × 30) + (x + 64) × 10 = 1640 
⇒ 30x + 10x + 640 = 1640 
⇒ 40x = 1000
⇒ x = 25

∴ The value of x is 25.
২৪.
A man and a boy received Tk. 820 as wages for 5 days for the work they did together. The man's efficiency in the work was thrice times that of the boy. What are the daily wages of the boy?
  1. ক
    ক) Tk. 40
  2. খ
    খ) Tk. 39
  3. গ
    গ) Tk. 41
  4. ঘ
    ঘ) None of the above
ব্যাখ্যা
Man = 3 boy
Daily wages for them = 820/5
                                   = 164
4 boy (1 man + 1 boy) = 164
4 boy = 164
Or, boy = Tk. 41
২৫.
If 5 boys write 5 pages in 5 minutes, then 3 boys will write 3 pages in -
  1. ক
    ক) 1 minute
  2. খ
    খ) 3 minutes
  3. গ
    গ) 5 minutes
  4. ঘ
    ঘ) 9 minutes
ব্যাখ্যা
If 5 boys write 5 pages in 5 minutes

Formula used:
Men × Time/Work = Men × Time/Work

Calculation:
According to the question,
⇒ (5 × 5)/5 = (3 × Time)/3
⇒ 5 minutes

∴ 3 boys will write 3 pages in 5 minutes.