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

1.

Tapas works twice as much as Mihir. If both of them finish the work in 12 days, Tapas alone can do it in: 

   A.) 20 days
   B.) 24 days
   C.) 18 days
   D.) 20 days

Answer: Option 'C'

Mihir = 2 Tapas (Consider, Tapas as ‘T’ and Mihir as “M”) 
So, T ×2 T/ T + 2T = 12 
2 T × T/3 T = 12 
2 T = 3 × 12 = 36 
T = 36/2 = 18 days i.e. No. of days taken by Tapas alone = 18 days.

2.

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.

3.

If A, B and C can do a job in 20, 30 and 60 days respectively. In how many days A can do the work if B and C help him on every third day?

   A.) 12 days
   B.) 15 days
   C.) 16 days
   D.) 18 days

Answer: Option 'B'

Efficiency of A = 1/20 = 5% per day
Efficiency of B = 1/30 = 3.33% per day
Efficiency of C = 1/60 = 1.66% per day
In three days A can do 15% of the job himself and B and C do 5% of the job ( 1.66% + 3.33% )
In three days they can do 20% of the job, to do 100% of the job, they need 3 × 5 = 15 days

4.

A and B together can plough a field in 10 hours but by himself A requires 15 hours. How long would B take to plough the same field? 

   A.) 10 hours
   B.) 20 hours
   C.) 30 hours
   D.) 40 hours

Answer: Option 'C'

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 No. of hours required by B = 10 × 15/ 15 – 10 = 150/5 = 30 hours.

5.

Ram and Shyam together can finish a job in 8 days. Ram can do the same job on his own in 12 days. How long will Shyam take to do the job by himself? 

   A.) 16 days
   B.) 20 days
   C.) 24 days
   D.) 30 days

Answer: Option 'C'

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 No. of days Shyam take to finish the job alone = 8 × 12/12 – 8 
= 8 × 12/4 = 24 days.

6.

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

7.

A completes a work in 12 days and B complete the same work in 24 days. If both of them work together, then the number of days required to complete the work will be 

   A.) 8 days
   B.) 6 days
   C.) 7 days
   D.) 5 days

Answer: Option 'A'

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 
Therefore, here, the required number of days = 12 × 24/ 36 = 8 days.

8.

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.

9.

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

10.

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? 

   A.) 13 1/3 days
   B.) 15 days
   C.) 20 days
   D.) 56 days

Answer: Option 'A'

A’s 8 day’s work = 1/40 × 8 = 1/5 
Remaining work = 4/5 
4/5 of the work is finished by Y in 16 days’ 
So, Y can finish the whole work alone in 16 ×5/4 days = 20days 
They both together can finish it in 40 × 20/60 =13 1/3 days.

11.

12 men work 8 hours per day to complete the work in 10 days. To complete the same work in 8 days, working 15 hours a day, the number of men required

   A.) 4 days
   B.) 5 days
   C.) 6 days
   D.) 8 days

Answer: Option 'D'

That is, 1 work done = 12 × 8 × 10 
Then, 12 8 × 10 = ? × 15 × 8 
? (i.e. No. of men required) = 12 × 8 × 10/15× 10 = 8 days.

12.

A can do a work in 4 days, B can do it in 5 days and C can do it in 10 days. A, B and C together can do the work in 

   A.) 1 3/5 days
   B.) 1 9/11 days
   C.) 2 5/6 days
   D.) 3 days

Answer: Option 'B'

When A, B and C can do a work in x, y and z days respectively. Then, the three of them 
together can finish the work in xyz/ x y + y z + x z days 
That is, A, B and C together ca do the work in 4 × 5 × 10/ 20 + 50 + 40 
= 4 × 5 × 10/110 = 20/11 = 1 9/11 days.

13.

The ratio of efficiency in  completing the task of A and B is 2 : 1. If both can complete the work in 10 days, in how many days B alone can complete the work. 

   A.) 30
   B.) 25
   C.) 20
   D.) 35

Answer: Option 'A'

Given, ratio of efficiency of A and B = 2 : 1
=> which means A is twice efficient as B
=> If A completes a work in x days, then B can complete the same work in 2x days.
=> B = 2A
=> A = B/2
=> A = 0.5 B
And A + B = 10
Subs A = 0.5B and A + B = 10 in the eqn 1/(A + B) = (1/A) + (1/B)
=> 1/ 10 = (1/0.5B) + (1/ B)
=> 1/ 10 = (1 + 0.5) / 0.5B
=> 1/ 10 = 1.5 / 0.5B
Taking reciprocal on both sides
=> 10 = 0.5B / 1.5
=> 0.5B = 10 * 1.5
=> B = 15 / 0.5
=> B = 30 days
Thus, B alone can complete the work in 30 days.

14.

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.

15.

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

   A.) 6 days
   B.) 10 days
   C.) 15 days
   D.) 20 days

Answer: Option 'B'

X’s 1 day’s work = 1/20 
X’s 4 day’s work = 1/20 × 4 = 1/5 
The remaining work = 4/5 
X and Y’s 1 day work = 1/20 + 1/12 = 4/30 = 2/15 
Therefore, Both together finish the remaining work in 4/5/2/15 days 
= 4/5 × 15/2 = 6 days 
Therefore, the total number of days taken to finish the work = 4 + 6 = 10 days.

16.

3 men or 5 women can do a work in 12 days. How long will 6 men and 5 women take to finish the work? 

   A.) 4 days
   B.) 10 days
   C.) 15 days
   D.) 20 days

Answer: Option 'A'

3 men = 5 women 
1 woman = 3/5 men 
So, 5 women = 3/5 × 5 = 3 men 
6 men and 5 women = 6 + 3 = 9 men 
1 work done = 3 men × 12 days 
3 × 12 = 9 × ? days 
? days = 3 × 12/9 = 4 days.

17.

A can do a piece of work in 5 days and B can do the same work in 10 days. How many days will both take to complete the work?

   A.) 5 days
   B.) 3 1/3 days
   C.) 3 days
   D.) 6 days

Answer: Option 'B'

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. 
That is, the required No. of days = 5 × 10/15 = 3 1/3 days.

18.

A and B together can complete a piece of work in 8 days while B and C together can do it in 12 days. All the three together can complete the work in 6 days. In how much time will A and C together complete the work? 

   A.) 8 days
   B.) 10 days
   C.) 12 days
   D.) 20 days

Answer: Option 'A'

A’s 1 day’s work = A + B + C’s 1 day’s work – B + C’s 1 day’s work = 1/6 – 1/12 = 1/12 
B’s 1 day’s work = A + B’s 1 day’s work – A’s 1 day’s work = 1/8 – 1/12= 1/24 
C’s 1 day’s work = B+ C’s 1 day’s work – B’s 1 day’s work = 1/12 – 1/24 = 1/24 
A +B’ 1 day’s work = 1/12 + 1/24 = 3/24 
Therefore, A and C together will finish the whole work in 24/3 = 8 days

19.

56 men completes a work in 12 days. How many men will be required to complete the work in 16 days?

   A.) 38
   B.) 24
   C.) 42
   D.) 48

Answer: Option 'C'

1 work done = 56 men × 12 days 
Then, 56 ×12 = ? men × 16 
? men = 56 × 12/16 = 42 men.

20.

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.


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