40 Time and Work Questions for CAT with Answers

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Question 21:
Samtaprasad can do a piece of work in 50 days. He worked only for 5 days and was infected with Malaria and had to leave the job. Shantaprasad completed the remaining work in 30 days. The number of days, in which both together can complete the work is
[1] 22 days
[2] 20 days
[3] 25 days
[4] 27 days

Answer:

Option: 2

Explanation:

Samtaprasad's 1 day work =, 1/50. 5 days work = (5/50) = 1/10.

=>Remaining work = 1 - (1/10) = 9/10.

As Shantaprasad completes 9/10 work in 30 days, so the work done by him in one day = 9/300. When they work together, the work done by them in one day = (1/50) + (9/300) = 1/20.

=>Number of days required by them, working together = 20.


Question 22:
25 days of Ram's wages can be paid by a certain sum of money. The same amount of money is sufficient to pay Badriprasad's wages for 20 days. The number of days for which the money will be sufficient to pay the wages of both if they work together is
[1] 10 days
[2] 11 days
[3] 100/9 days
[4] 110/9 days

Answer:

Option: 3

Explanation:

Ram's 1 day's wages = 1/25th of the money, Badriprasad's 1 day's wages

= 1/20th of the money. (Ram + Badriprasad)'s 1 day's wages

= 1/25 + 1120 = 9/100 of the total money. Hence the money will be sufficient

for 100/9 days if both of them work together.


Question 23:
Gagan is thrice as good a worker as Dilip and takes 8 days less to do a piece of work than Dilip. In how many days can Dilip do the complete work?
[1] 4 days
[2] 24 days
[3] 12 days
[4] 18 days

Answer:

Option: 3

Explanation:

Let Dilip's 1 day's work = X Gagan's 1 day's work = 3X.

Total time taken by Dilip to do the whole job = 1/X.

Total time taken by Gagan to do the whole job = 1/3X.

It is given that 1/3X + 8 = 1/X X = 1/12 = Dilip's one day's work.

Time taken by Dilip to complete the whole work alone = 12 days.


Question 24:
Billy is four times as good a workman as Silly and can build a wall in 45 days less than the number of days required by Silly. What is the time they will take, working together, to build two such walls?
[1] 12 days
[2] 24 days
[3] 9 days
[4] 18 days

Answer:

Option: 2

Explanation:

Let Billy's time to complete one work = x days.

Then, Silly's time to complete one work = 4x days.

Since Billy take 45 days less than Silly to build a wall.

i.e., 4x - x = 45 => x = 15 and 4x = 60.

Working together they will take \(\frac{1}{{\frac{1}{{15}} + \frac{1}{{60}}}} = 12\) days to build one wall.

So, to build two such walls, 24 days will be required.


Question 25:
X men can finish a job in 40 days. If 5 extra Men join them, the job takes 10 days less. What is the value of X?
[1] 15
[2] 20
[3] 10
[4] 18

Answer:

Option: 1

Explanation:

Work = W. Let the number of men be X.

40X = W and (40 - 10)(X + 5)

= W => 40X = 30(X + 5) => 10X = 150=> X = 15.


Time and Work

40 Time and Work Questions for CAT with Answers
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