Time and Work :(96) MCQs with Answers

1.

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.

2.

A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 a.m. while machine P is closed at 11 a.m. and the remaining two machines complete the work. Approximately at what time will the work be finished?

   A.) 11: 30 a.m.
   B.) 12 noon
   C.) 12:30 p.m
   D.) 1 p.m.

Answer: Option 'D'

The three machines 1 hour’s work = 1/8 + 1/10 + 1/12 = 37/120
Their, work from 9 a.m. to 11 a.m. = 2 hour’s work = 37/120 × 2= 27/60 
The remaining work = 23/60 
Machines Q and R’s 1 hours work = 1/10 + 1/12 = 11/60 
Therefore, the time taken by Q and R to finish the remaining 23/60 work = 23/60/11/60 
= 23/60 × 60/11 = 23/11 = 2 hours approx. 
Therefore, the approximate time at which the work is finished = 11 + 2 = 1 p.m.

3.

Rajesh and Ajay can complete a job in 16 days. Rajesh alone can do it in 24 days. How long will Ajay alone take to finish the whole work? 

   A.) 20 days
   B.) 48 days
   C.) 30 days
   D.) 36 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. 
Then, Ajay alone can finish the whole work in, 16 × 24/24 – 16 = 16 × 24/8 = 48 days.

4.

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

5.

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.

6.

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.

7.

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.

8.

8 children and 12 men complete a certain piece of work in 9 days. Each child takes twice the time taken by a man to finish the work. In how many days will 12 men finish the same work?

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

Answer: Option 'C'

8 children = 4men 
Then, 4 + 12 = 16 men completes the job in 9 days 
Then, 16 × 9 = 12 × ? days 
? days = 16 × 9/12 = 12 days.

9.

A can do a piece of work in 12 days, while B can do it in 8 days with the help of C, they finish the work in 4 days. Then C alone can do the work in 

   A.) 24 days
   B.) 20 days
   C.) 16 days
   D.) 4 days

Answer: Option 'A'

A and B together can do the work in 12 × 8/20 = 96/20 days 
A +B and C together do the work in 4 days. 
Then C alone can do the work in 96/20 × 4/96/20 – 4 days 
= 96/5/16/20 = 96/5 × 20/16 = 24 days.

10.

10 men can complete a piece of work in 15 days and 15 women can complete the same work in 12 days. If all the 10 men and 15 women work together, in how many days will work get completed? 

   A.) 6
   B.) 7 2/3
   C.) 6 2/3
   D.) 6 1/3

Answer: Option 'C'

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. 
Here, men’s working days can be taken as A and that of women as B 
Then, 15 × 12/27 = 6 2/3 days.

11.

A can complete a job in 9 days, B in 10 days and C in 15 days. B and C start the work together and are forced to leave after 2 days. The time taken to complete the remaining work is 

   A.) 13 days
   B.) 10 days
   C.) 9 days
   D.) 6 days

Answer: Option 'D'

A’s 1 day work = 1/9 
B’s 1 day work = 1/10 
C’s 1 day work = 1/15 
B + C ‘ s 1 day work = 1/10 + 1/15 = 1/6 
B + C’s 2 day’s work = 1/6 × 2 = 1/3 
The work remaining = 1 – 1/3 = 2/3 
A can do the full work in 9 days. 
So, the remaining 2/3 of the work is done by A in 2/3 × 9 days = 6 days.

12.

If 40 men working 9 hours a day can finish a work in 21 days, in how many days will 27 men working 10 hours a day do the same work? 

   A.) 20 days
   B.) 28 days
   C.) 29 days
   D.) 25 days

Answer: Option 'B'

That is, 1 work done = 40 × 9 × 21 
Then, 40 × 9 × 21 = 27 × 10 × ? days 
Therefore, ? days = 40 × 9 × 21 /27 × 10 = 28 days. 
= 4 hours.

13.

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

14.

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.

15.

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: 

   A.) 8 days
   B.) 10 days
   C.) 12 days
   D.) 15 days

Answer: Option 'C'

No. of days taken by them working together = 15 × 10/25 = 6 days 
Their 1 day’s work = 1/6 
Their 2 day’s work = 1/6 × 2 = 1/3 
The work remaining = 2/3
A’s 1 day work = 1/15 
Time taken by A to finish 1/3 of the work = 2/3/1/15 = 2/3 ×15 = 10 days
Therefore, the total number of days taken to finish the whole work = 10 +2 = 12 days.

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