Time and Work :(96) MCQs with Answers

1.

Two tapes can fill an empty tank in 12 and 15 minutes respectively. If both the taps are opened simultaneously in how many minutes the tank would be full.

   A.) 21 / 5 minutes
   B.) 20/3 minutes
   C.) 21 / 4 minutes
   D.) 23/3 minutes

Answer: Option 'B'

Let the two taps be A and B.
Given, Tap A fill the tank in 12 mins
Tap B fill the tank in 15 mins

To find the Time taken by both taps opened together to fill the tank:
1/(A + B) = (1/A) + (1/B)
=> 1/(A + B)= (1/ 12) + (1/ 15)
=> 1/(A + B)= 27 / 180

Taking reciprocal on both sides
=> A + B = 180 / 27
=>A + B = 20 / 3 mins

2.

The rates of working of A and B are in the ratio 3 : 4. The number of days taken by them to finish the work are in the ratio: 

   A.) 3 : 4
   B.) 9 : 16
   C.) 4 : 3
   D.) 3 : 2

Answer: Option 'C'

The No. of days taken by them = inverse ratio = 4 : 3.

3.

A and B working together can complete a work in 12 days, B and C working together will complete the work in 15 days, C and A working together can complete the work in 20 days. If all three work together, in how many days the work can be completed?

   A.) 10 days
   B.) 8 days
   C.) 13 days
   D.) 12 days

Answer: Option 'A'

Given
A + B 's one day work will be 1/12
Similarly, B + C's one day work will be 1/15
C + A 's one day work be 1/20
A + B = 1/12 ----> (1)
B + C = 1/15 ----> (2)
C + A = 1/20 ----> (3)
Adding all the above equation we get
2(A+B+C) = 1/12 + 1/15 + 1/20
=> 5/60 + 4/60 + 3/60
=> 12/60
A+B+C = 12 / 120
= 1/10
If all three work together, the work will be completed in 10 days.

4.

Ram, Shyam and Mohan can do a piece of work in 12, 15 and 20 days respectively. How long will they take to finish it together?

   A.) 10 days
   B.) 12 days
   C.) 14 days
   D.) 5 days

Answer: Option 'D'

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 
Therefore, the No. of days taken by them together to finish the whole work 
= 12 × 15 × 20/12 × 15 + 15 × 20 + 12 × 20 
= 12 × 15 × 20/720 = 5 days.

5.

A and B can do a job together in 7 days. A is 1 ¾ times as efficient as B. the same job can be done by A alone in:

   A.) 9 1/3 days
   B.) 11 days
   C.) 12 ¼ days
   D.) 16 1/3 days

Answer: Option 'B'

1 ¾ = 7/4 
7/4 A = B, replacing B by 7/4 A, we get 
A × 7/4 A/ A + 7/4 A = 7days 
7 A × A/4 / 11A/4 = 7 A × A/ 11 A = 7A /11 = 7 
A = 77/7 = 11, So, A alone can finish the work in 11 days.

6.

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.

7.

Kiran can complete a work in 45 days. Kishore completes the same work in 40 days. They both started the work Kiran left the work after some days. Kishore completed the remaining work in 23 days. Then after how many days Kiran left the work? 

   A.) After 10 days
   B.) After 7 days
   C.) After 9 days
   D.) After 6 days

Answer: Option 'C'

(x/45) + (x/40) + (23/40) = 1
(x/45) + (x/40) = 1 - (23/40)
(8x + 9x)/360 = 1 - (23/40)
17x/360 = 17/40
x = 9
After 9 days

8.

A and B together finish a work in 30 days they worked for it for 20 days and then B left. The remaining work was done by A alone in 20 more days. B alone can finish the work in 

   A.) 48 days
   B.) 50 Days
   C.) 54 Days
   D.) 60 Days

Answer: Option 'D'

(A + B)’s 1 days work = 1/30 
A+B ‘s 20 days work = 1/30 × 20 = 2/3 
Remaining work = 1 -2/3 = 1/3
1/3 of the work is done by A in 20 days 
Therefore, A can complete the full work in 3 × 20 = 60 days 
So, A’s 1 day’s work = 1/60 
Then, B’s 1 day work = 1/30 – 1/60 = 1/60 
Therefore, B can complete the work in 60 days.

9.

A does 20% less work than B. if A can complete a piece of work in 7 ½ hours, then B can do it in 

   A.) 5 hours
   B.) 5 ½ hours
   C.) 6 hours
   D.) 6 ½ hours

Answer: Option 'C'

B can finish the work in 80% of 7 ½ hours of time 
7 ½ = 15/2 
Therefore, time taken by B = .8 × 15/2 = 30/5 = 6 hours.

10.

If 4 workers can make 42 toys in 6 days, how many toys can 12 workers make in 3 days?

   A.) 63
   B.) 28
   C.) 252
   D.) 7

Answer: Option 'A'

4 workers in 3 days make 21 toys, 
Then, 1 worker can make 21/4 toys in 3 days 
Therefore, No. of toys made by 12 workers in 3 days = 21/4 × 12 = 63 toys.

11.

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.

12.

If 3 persons can do 3 times of a particular work in 3 days, then, 7 persons can do 7 times of that work in 

   A.) 7 days
   B.) 6 days
   C.) 4 days
   D.) 3 days

Answer: Option 'D'

That is, 1 person can do one time of the work in 3 days. 
Therefore, 7 persons can do 7 times work in the same 3 days itself.

13.

Three workers working all days can do a work in 10 days. But one of them having other employment can work only half time. In how many days the work can be finished? 

   A.) 15 Days
   B.) 24 Days
   C.) 16 Days
   D.) 12 Days

Answer: Option 'D'

Sum of each persons’ one day’s work = 1/3 ×10 + 1/3 ×10 + 1/3× 20 = 1/30 + 1/30 + 1/60 
= 5/60 = 1/12 
Therefore, the work can be finished in 12 days.

14.

Kamal can do a work in 15 days. Bimal is 50% more efficient than Kamal. The number of days, Bimal will take to do the same piece of work, is 

   A.) 10
   B.) 10 ½
   C.) 12
   D.) 14

Answer: Option 'A'

Kamal’s 15 days is 150% of No. days taken by Bimal to finish the job.
Therefore, the No. of days taken by Bimal = 15/150 × 100 = 10 days

15.

A job can be completed by 12 men in 12 days. How many extra days will be needed to complete the job if 6 men leave after working for 6 days? 

   A.) 12
   B.) 10
   C.) 8
   D.) 6

Answer: Option 'D'

Half the work is done by 12 men in 6 days. 
Remaining half should be done by 6 men in ? days 
Then, 12 × 6 × ½ = 6 × ?days × ½ 
36 = 3 × ?days
? days = 36/3 =12 days 
Extra days required = 12 -6 = 6 days.

16.

Sam, Bob and Kim can do a job alone in 15 days, 10 days and 30 days respectively. Sam is helped by Bob and Kim every third day. In how many days will the job be completed? 

   A.) 9 days
   B.) 8 1/3 days
   C.) 8 days
   D.) 6 1/3 days

Answer: Option 'A'

The work done by the three persons in 3 days ( because Sam works only on every third day) 
= 3/15 + 1/10 + 1/30 = 6 + 3 + 1/30 = 10/30 
= 1/3 of the work 
Therefore, the job will be completed in 3 × 3 = 9 days.

17.

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.

18.

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

19.

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:

   A.) ¼
   B.) 1/10
   C.) 7/15
   D.) 8/15

Answer: Option 'D'

Working together, the No. of days taken by them to finish the work = 15 × 20/35 
= 60/7 days
Then, their 1 day’s work = 7/60 
Their, 4 days work = 7 × 4/60 = 7/15 of the total work 
Therefore, the fraction of the work, that is left = 1- 7/15 = 8/15.

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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