RRB NTPC - Time and Work :(96) MCQs with Answers

1.

A particular job can be completed by a team of 10 men in 12 days. The same job can be completed by a team of 10 women in 6 days. How many days are needed to completed the job if the two teams work together? 

   A.) 4
   B.) 6
   C.) 18
   D.) 9

Answer: Option 'A'

Consider men’s work days as one group and women’s working days as other group Then, the required No. of days = 12 × 6/18 = 4 days.

2.

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: 

   A.) 4 days
   B.) 6 days
   C.) 8 days
   D.) 18 days

Answer: Option 'A'

That is, if b alone can finish the work in 12 days, 
A alone can finish the work in 6 days.
If A can complete a work in x days and B can complete the same work in y days, then, both of them together can complete the work in x y/ x+ y days. 
A and B can together finish the work in 6 × 12/18 days = 4 days.

3.

Alan can complete a work in 10 days B is 25% more efficient than A. In how many days B and A together can complete the work.

   A.) 15 / 7 days
   B.) 15 / 4 days
   C.) 15 / 2 days
   D.) 5 days

Answer: Option 'B'

A completes in 10 days
B completes in 6 days.
A + B 1 day work = (1/10 + 1/6) = (3+5) /30 = 8 / 30 = 4 / 15
A + B can complete in 15 / 4 days

4.

If 8 men or 12 women can do a piece of work in 10 days, then the number of days required by 4 men and 4 women to finish the work is

   A.) 8
   B.) 10
   C.) 12
   D.) 14

Answer: Option 'C'

8 men = 12 women 
1 woman = 8/12 men = 2/3 men 
4 women = 2/3 × 4 men = 8/3 men 
4 men + 4 women = 4 + 8/3 men = 20/3 men 
1 work done = 8 × 10 
8 × 10 = 20/3 × ?days 
? days = 8 × 10 × 3/20 = 12 days.

5.

39 men can repair a road in 12 days working 5 hours a day. In how many days will 30 men working 6 hours peer day complete the work?

   A.) 10
   B.) 13
   C.) 14
   D.) 15

Answer: Option 'B'

1 work done = 39 × 12 × 5 
39 × 12 × 5 = 30 × 6 × ? days
? days = 39 × 12 × 5/ 30 × 6 = 13 days.

6.

Six men or tern boys can do a piece of work in fifteen days. How long would it take for 12 men and 5 boys to do the same piece of work? 

   A.) 6 days
   B.) 28 days
   C.) 25 days
   D.) 7 days

Answer: Option 'A'

6 men = 10 boys 
Then, 1 boy = 6/10 men = 3/5 men 
Then, 5 boys = 3/5 × 5 = 3 men 
12 men + 5 boys = 15 men 
1 work done = 6 men × 15 days 
Therefore, 6 × 15 = 15 × ? days 
? days = 6 × 15/15 = 6 days.

7.

A and B can do a piece of work in 4 days. If A can do it alone in 12 days, B will finish the work in

   A.) 4 days
   B.) 6 days
   C.) 8 days
   D.) 10 days

Answer: Option 'B'

If A and B together can do a piece of work in x days and A alone can do the same work in y 
days, then B alone can do the same work in x y/ y – x days. 
Therefore, the number of days B will take to finish the work = 4 × 12/ 12 – 4 
= 48/8 = 6 days.

8.

30 labourers working 7 hours a day can finish a piece of work in 18 days. If the labourers work 6 hours a day, then the number of labourers required to finish the same piece of work in 30 days will be 

   A.) 15 days
   B.) 21 days
   C.) 25 day
   D.) 22 day

Answer: Option 'B'

That is, 1 work done = 30 × 7 ×18 = ? × 6 × 30 
? (No. of labourers) = 30 × 7 × 18/6 × 30 = 21

9.

A and B can do a piece of work in 45 days and 40 days respectively. They began to do the work together but A leaves after some days and then B completed the remaining work in 23 days. The number of days after which A left the work was: 

   A.) 6
   B.) 8
   C.) 9
   D.) 12

Answer: Option 'C'

A and B together can finish the work in 45 × 40/85 = 360/17 days 
A and B’s 1 day’s work = 17/360 
A’s 1 day’s work = 1/45 
B’s 1 day’s work = 1/40 
B’s 23 day’s work 1/40 × 23 = 23/40 
Remaining work = 1 – 23/40 = 17/40 
17/40 of the work is done by A and B together 
17/40 of the work is done by A and B together in = 17/40/17/360 = 17/40 × 360/17 days 
= 9 days
Therefore, A left after 9 days.

10.

A work could be completed in 100 days. However, due to the absence of 10 workers, it was completed in 110 days then, the original number of workers was 

   A.) 100
   B.) 110
   C.) 55
   D.) 50

Answer: Option 'B'

Let ‘x’ be the original number of workers 
Then, x × 100 = ( x – 10) 110 
100 x = 110x – 1100 
1100 = 10 x 
x = 110.

11.

Raju can complete a work in 30 days. Ajay completes the same work in 20 days. They both started the work Raju left the work after some days. Ajay completed the remaining work in 15 days. Then after how many days Raju left the work?

   A.) 4 days
   B.) 5 days
   C.) 3 days
   D.) 6 days

Answer: Option 'C'

(x/30) + (x/20) + (15/20) = 1
(2x + 3x)/60 = 1 - (15/20)
5x/60 = (20 - 15)/20
5x/60 = 5/20 
x/3  = 1
x = 3 days
After 3 days

12.

A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days? 

   A.) 11 days
   B.) 13 days
   C.) 20 3/17 days
   D.) 14 days

Answer: Option 'B'

The ratio of their efficiency = A : B = 130 : 100 = 13 : 10 
Therefore, the ratio of the time taken by them = 10 : 13 
A takes 23 days = 10 units of ratio 
So, 1 unit of ratio = 23/10 
Time taken by B alone to finish the work = 23/10 ×13 = 29.9 = 30 days 
Therefore, the No. of days taken to finish the work working together = 23 × 30/ 53 
= 13 days

13.

Aravindh is twice efficient as Rakesh. If both work together and complete a work in  10 days, find the number of days Aravindh will take to complete the work. 

   A.) 30
   B.) 15
   C.) 45
   D.) 60

Answer: Option 'B'

Let the time taken by Aravindh = A days
the time taken by Rakesh= R days

Given, Aravindh is twice efficient as Rakesh
=> If Aravindh completes a work in x days, then Rakesh can complete the same work in 2x days.
=> R = 2A

Given, A + R = 10 days
=> 1/(A + R) = (1/A) + (1/R)
=> 1/ 10 = (1/A) + (1/2A)
=> 1/ 10 = 3 / 2A
Taking reciprocal on both sides
=> 10 = 2A/3
=> 2A = 30
=> A = 15 days
Thus, Aravindh completes a work in 15 days

14.

A can do 1/3 of a work in 5 days and B can do 2/5 of the work in 10 days. In how many days both A and B together can do the work?

   A.) 7 ¾
   B.) 8 4/5
   C.) 9 3/8
   D.) 10

Answer: Option 'C'

A can do finish the whole work in 3 × 5 days = 15 days
B can finish the whole work in 5 /2 × 10 days = 25 days 
A and B together can finish the work in 15 × 25/ 40 days = 9 3/8 days.

15.

If 8 men can dig a well in 18 days, then the number of days, 12 men will take to dig the same well will be

   A.) 12 days
   B.) 10 days
   C.) 8 days
   D.) 16 days

Answer: Option 'A'

Work done = 8 × 18 
Then, 8 × 18 = 12 × ? days 
? days = 8 × 18/12 = 12 days

16.

5 men can do a piece of work in 6 days while 10 women can do it in 5 days. In how many days can 5 women and 3 men do it?

   A.) 4
   B.) 5
   C.) 6
   D.) 8

Answer: Option 'B'

5men × 6 = 10 women × 5 
30 men = 50 women 
1 woman = 30/50 men = 3/5 men 
5 women = 3/5 × 5 men = 3 men 
5 women + 3 men = 3 + 3 = 6 men 
That is, 1 work done = 5 × 6 
5 × 6 = 6 × ?days 
? days = 5 × 6/6 = 5 days.

17.

A and B together can complete a work in 3 days. They start together. But, after 2 days, B left the work. If the work is completed after 2 more days, B alone could do the work in 

   A.) 5 days
   B.) 6 days
   C.) 9 days
   D.) 10 days

Answer: Option 'B'

A and B’s 1 day’s work = 1/3 
Their 2 day’s work = 1/3 × 2 = 2/3 
Remaining work = 1/3 
1/3 of the work is finished by A in 2 days 
Then, the whole work can be finished by A alone in 3 × 2 = 6 days 
So, A’s 1 day’s work = 1/6 
Therefore, B’s 1 day’s work = 1/3 – 1/6 = 1/6 
Therefore, the whole work can be done B alone in 6 days.

18.

Somu and Ramu can complete the work in 20 and 30 days respectively. In how many days, 50% of the work will get completed?

   A.) 5
   B.) 6
   C.) 6.5
   D.) 7.5

Answer: Option 'B'

Let the time taken by Somu= A = 20 days
the time taken by Ramu= B = 30 days
Then number of days to complete 100% of work by Somu+ Ramutogether:
=>1/(A + B) = (1/A) + (1/B)
=> 1 / (A + B) = (1 / 20) + (1 / 30)
=> 1 / (A + B) = (30 + 20) / (20 × 30)
=> 1 / (A + B) = 50 / 600
Taking reciprocal on both sides
A + B = 600/50
A + B = 12 days
Thus 100% of the work is completed in 12 days,
50% of the work is completed in {(12 / 100%) × 50%} days = 6 days

19.

Vamsi and Vivek can complete a piece of work in 30 and 15 days repectively by working alone. After how many days 80% of the work would have got completed? 

   A.) 8 days
   B.) 12 days
   C.) 14 days
   D.) 10 days

Answer: Option 'A'

Let the time taken by Vamsi = A days = 30 days
the time taken by Vivek = B days = 15 days

Vamsi + Vivek together can complete 100 % of the work in:
=> 1/(A + B) = (1/A) + (1/B)
=> 1 / (A + B) = (1 / 30) + (1 / 15)
=> 1 / (A + B) = (15 + 30) / (30 * 15)
=> 1 / (A + B) = 45 / 450
Taking reciprocal on both sides
A + B = 450/45
A + B = 10 days

Thus 100% of the work is completed in 10 days,
80% of the work is completed in {(10 / 100%) × 80%} days = 8 days

20.

A and B can complete a given work by working together in 8 days. B takes twice the number of days to complete the work compared to A. In how many days A can finish the work by working alone? 

   A.) 16
   B.) 12
   C.) 14
   D.) 18

Answer: Option 'B'

Let the time taken by A to finish the work = x days
Then, time taken by B to finish the work = 2x days

Given, Time taken by A and B together ie., (A + B) = 8 days.
=>1/(A + B) = (1/A) + (1/B)
=> 1/8 = (1/x) + (1/2x)
=> 1/8 = (2 + 1) / 2x
=> 1/8 = 3/2x
Taking reciprocal on both sides,
=> 8 = 2x / 3
=> 8 * 3 = 2x
=> 24/ 2 = x
=>x = 12
A alone complete the work in 12 days.


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