Time & Work Questions for CAT with Answers PDF

A = 10%, B = 5% and Combined work is 20%. Hence, C’s work is 5% and will require 20 days

Ajay + Vijay = 1/28 and Ajay + Vijay + Manoj = 1/21.

Hence, Manoj = 1/21 – 1/28 = 1/84.

Hence, Manoj will take 84 days to do the work.

Total work = 15 * 210 = 3150 mandays. After 100 days, work done = 15 * 100 = 1500 mandays. Work left = 3150 – 1500 = 1650 mandays. This work has to be done with 30 men working each day. The number of days (more) required = 1650/30 = 55 days.

A’s work = 10% B’s negative work = 6.66% (A + B)’s work = 3.33%To fill a half empty tank, they would take 50/3.33 = 15 hours

The capacity of the tank

= LCM(10, 20 and 25) = 100

Efficiency of A = 100/10 = 10

Efficiency of B = 100/20 = 5

Efficiency of C = 100/25 = 4

Tank filled in 2 hours by A, B, and C

= (10 + 5 + 4) × 2 = 38 unit

According to the question, 

After 4 hours from the beginning, tap B is also closed

Tank filled in 2 hours by A & B

= (10 + 5) × 2 = 30 unit

Now, tap B is also closed

Remiang capacity of tank = 100 - 38 - 30 = 32 unit

These 32 unit is filled by A alone.

So, the total work done by A 

= Work done in (1st 2 hr + next 2 hr + 32 unit)

= 10 × 2 + 10 × 2 + 32 = 72 unit

Percentage of a tank filled by A = (72/100) × 100 = 72%.

Hence, The Required value is 72%.

In 6 days A would do 25% of the work and in 8 days B would do 25% of the work himself. So, C has to complete 50% of the work by himself. In all C would require 30 days to do 50% of the work. So, he would require 22 more days.

Let n be the number of metres planned per day. Start from the options to find the number of planned days. In the options the 2 feasible values are 30 metres and 27 metres (as these divide 270).

Suppose we check for 30 metres per day, the work would have got completed in 9 days as per the original plan. In the new scenario: 3n + 5(n + 8) = 280 -> n = 30 too. Hence, this option is correct.

Note that if we tried with 27 metres per day the final equation would not match as we would get: 3n + 6(n + 8) = 280 -> which does not give us the value of n as 27 and hence this option is rejected.

A's 1 day's work =1/15

B's 1 day's work =1/20

(A + B)'s 1 day's work =1/15+1/20=7/60

(A + B)'s 4 day's work = 7/60 * 4 = 7/15

Therefore, Remaining work =1- 7/15 =8/15

In three days, the work done will be 25 + 16.66 + 30 = 71.66%. The remaining work will get done by Y in 28.33/5.55 = 5.1 days. [Note: You need to be fluent with your fraction to percentage conversions in order to do well at these kinds of calculations.]

Since the first typist types for 4 minutes and the second typist types for exactly 6 minutes, the work left (which is given as 1/5 of the total work) would be the work the first typist can do in 2 minutes.

Thus, the time taken by the first typist to do the work would be 10 minutes and his rate of work would be 10% per minute. Also, since both the typists can do the work together in 6 minutes, their combined rate of work would be 100/6 = 16.66% per minute.

Thus, the second typist’s rate of work would be 16.66 – 10 = 6.66% per minute.

He would take 100/6.66 = 15 minutes to complete the task alone.

0.5(A + B + C) = 50% of the work. Means  A, B and C can do the full work in 1 hour. Thus, (A + B + C) = 100% From this point it is better to solve through options. Option (c) gives the correct answer based on the following thought process. If c = 50% work per hour, it means C takes 2 hours to complete the work. 
Consequently, A would take 3 hours and hence do 33.33% work per hour. Since, A + B + C = 100%, this gives us B’s hourly work rate = 16.66%. For this option to be correct these nos. should match the second instance and the information given there. According to the second condition: A + 4B should be equal to 100%. Putting A = 33.33% and B = 16.66% we see that the condition is satisfied. Hence, this option is correct.

The per day digging of all three combined is 54 metres. Hence, their average should be 18. This means that the first should be 18 – x, the second, 18 & the third 18 + x.

The required conditions are met if we take the values as 15, 18 and 21 metres for the first, second and third diggers, respectively.

Hence, (a) is the correct answer

Let total work be 60 units. 1st tap fills 3units per minute, 2nd tap fills 4 units per minute and waste pipe empties 5 units per minute. So, when opened together all three will fill (3 + 4 – 5) = 2 units per min.

Hence in first 9 min, 18 units of tank is filled. Since the waste pipe is closed

∴ The remaining 42 units will require 42 /3 +4  = 6 min to fill.

Let the work done by a man, a woman and a child in a day be m, w and c respectively. Then, m = 3c and w = 2c ∴ 20m + 30w + 36c = 60c + 60c + 36c = 156c

Total units of work done in second case = (15m + 21w + 30c) × 7 × 18 = (45c + 42c + 30c) × 7 × 18 = 117c × 7 × 18

Hence, the required total ways 78 /156c = × 117c × 7 × 18 = Rs. 7,371.

Let Ajit’s rate of work be 100/2 = 50 work units per day. Baljit would do 100/3 = 33.33 work units per day and Diljit does 133.33/5 = 26.66 units of work per day.

Their 1 days work = 50 + 33.33 + 26.66 = 110 units of work per day.

In 20 days, the total work done would be 2200 units of work and hence for Baljit to do it alone it would take: 2200/33.33 = 66 days to complete the same work

Solve this using options.

If we check for option (c), i.e., the work of a man exceeds the work of a woman by 5 times, we would get the following thought process: Total work = 6 days * (3 women + 2 men) = 18 woman days + 12 man days = 18 woman days + 60 woman days = 78 woman days.
Thus, 9 women would take 78/9 days = 8.66 days and hence 3 men should do the same work in 3.66 days.
This translates to 3* 3.66 = 10 man days or 50 woman days which is incorrect as the number of woman days should have been 78. Thus, we can reject this option.

If we check for option (d), i.e., the work of a man exceeds the work of a woman by 6 times, we would get the following thought process: Total work = 6 days * (3 women + 2 men) = 18 woman days + 12 man days = 18 woman days + 72 woman days = 90 woman days.
Thus, 9 women would take 90/9 days = 10 days and hence 3 men should do the same work in 5 days.
This translates to 3 * 5 = 15 man days or 90 woman days which is correct as the number of woman days should be 90.

Let the capacity of the tank be 180 units. (LCM of 10, 12, 15 and 18) Amount of water drawn in one minute by Outlet Pipe A = 18 Units
Outlet Pipe B = 15 Units Outlet Pipe C = 12 Units
Outlet Pipe D = 10 Units
Let the total time taken to empty the tank with the given conditions be ‘t’ minutes. Amount drawn by A = 1 × 18 = 18 units
Amount drawn by B = 2 × 15 = 30 units
Amount drawn by C = (t–5) × 12 = (12t – 60) units
Amount drawn by D = t × 10 = 10t units
⇒ 18 + 30 + 12t – 60 + 10t = 180 22t = 192 or
t = 96 /11 minutes
=