Time & Work Questions for CAT with Answers PDF

Let A, B and C individually take a, b and c days to complete the same task, respectively.
B and C can finish the task in 6 days working together.
Therefore,

Again, two days of work of B and C equals to 3 days of A's work.
Therefore,

From equation (i),
3/a = 2/6 
a = 9 days
Now, A and B work for first two days and A and C work for last three days to complete the same task.
Therefore,

Substitute values of a and from equation (ii).

c = 9 days
Substitute values of a and c in equation (i).

b = 18 days
Hence, this is the required solution.

Let the initially formed hole empty the tank in x hours.
After getting the cross section doubled, it empties the tank in x/2 hours.
Inlet tap can fill 1/30th of the tank in 1 hour.
So, in 40 hours,  

⇒ x = 195 hours
If the cross section of the hole does not change at t = 10,
suppose the tank will fill in t hours.

The part of tank filled by Pipe A in 1 minute = 1/20
The part of tank filled by Pipe B in 1 minute = 1/30
The part of tank emptied by Pipe C in 1 minute = 1/15
So, totally in 3 minute (because open for 1 minute each) = 1/20 + 1/30 - 1/15 = 1/60
Consider 55/60 can be filled in 3 × 55 = 165 minute, remaining part is 1/12.
A can fill 1/20 in 1 minute.
So, capacity left is, (1/12) - (1/20) = 1/30
B can fill the remaining 1/30 in 1 minute.
So, total time taken = ((3 × 55) + 1 + 1) = 167 minute
Hence, it will take 167 minutes to fill the tank.

Let 4x be the total number of labourers.
4x labourers' work in half a day = 2x labourers' work in one day
Half of 4x, i.e. 2x labourers' work in second half of the day = x labourers' work in one day
According to given information, at the end of the day, the larger wall is completed.
Total 3x labourers are required to work full day to complete the work.
For smaller wall:
2x labourers' work in second half of the day = x labourers' work in one day
But, at the end of the first day, it was not completed and needed one labourer's full-day work.
Therefore, total number of labourers required for smaller wall = x + 1
x + 1 is half of the 3x.
x + 1 = 3x/2
x = 2
Total number of labourers who worked on the first day = 4 × 2 = 8

Let work done by A in 1 day be A, and that done by B in 1 day be B.
Let total work be W.
While working together, A and B took 24 days to complete the work. Therefore, we have
24(A + B) = W ...(i)
Also, as A received 50% more money than B, it is fair enough to assume that A must have done 1.5 times as much work in the same time as B.
Thus, A = 1.5B ...(ii)
Now, plugging the value of A as 1.5B from equation (ii) into equation (i), we have 24(2.5 B) = W or B = W/60 ...(iii)
Suppose, B took d days to do the same work alone.
Thus, dW/60 = W, or d = 60
Thus, working alone, B would take 60 days to do the work.
Hence, answer option (4) is correct.

After 1 minute, 40 litres is filled.
After 2 minutes, another 30 litres is filled (total 70 litres).
After 3 minutes, 20 litres is emptied.
Therefore, at the end of 3 minutes, 50 litres is filled.
50 litres is filled in 3 minutes.
Pipe A fills the tank at the rate of 40 litres a minute.
Pipe B at the rate of 30 litres a minute and Pipe C drains the tank at the rate of 20 litres a minute.
If each of them is kept open for a minute in the order A - B - C, the tank will have 50 litres of water at the end of 3 minutes. After 13 such cycles, the tank will have 13 × 50 = 650 litres of water.
It will take 13 × 3 = 39 minutes for the 13 cycles to be over. At the end of the 39th minute, Pipe C will be closed and Pipe A will be opened. It will add 40 litres to the tank. Therefore, at the end of the 40th minute, the tank will have 650 + 40 = 690 litres of water.

Interpretation of the first row of the first table in the question: 
Design and Development requires 30 expert man- days or 60 non-expert man-days.
Hence, work done in 1 expert man-day = 3.33% and work done in 1 non-expert man-day = 1.66%. Further, from the second table, it can be interpreted that: A is an expert at design and development. Hence, his work rate is 3.33% per day and B, D and E are ready to work as non-experts on design and development, hence their work rate is 1.66% per day each.
Thus, in 1 day the total work will be 
A + B + D + E = 3.33 + 1.66 + 1.66 + 1.66 = 8.33% 
work.
Thus, 12 days will be required to finish the design and development phase.

Interpretation of the first row of the first table in the question: 
Design and Development requires 30 expert man- days or 60 non-expert man-days.
Hence, work done in 1 expert man-day = 3.33% and work done in 1 non-expert man-day = 1.66%. Further, from the second table, it can be interpreted that: A is an expert at design and development. Hence, his work rate is 3.33% per day and B, D and E are ready to work as non-experts on design and development, hence their work rate is 1.66% per day each.
Thus, in 1 day the total work will be 
A + B + D + E = 3.33 + 1.66 + 1.66 + 1.66 = 8.33% 
work.
Thus, 12 days will be required to finish the design and development phase.
Increase of number of days 

For these questions, since food is no longer a constraint, the constraint then becomes the number of lives. Then, the assumption will be that the resistance lasts for one month with a loss of either 2000 sepoys, 2000 mantris or 1000 footies.
Length of resistance 

= 250 months.

For these questions, since food is no longer a constraint, the constraint then becomes the number of lives. Then, the assumption will be that the resistance lasts for one month with a loss of either 2000 sepoys, 2000 mantris or 1000 footies.
In 6 months, the resistance will have lost 12000 mantris. He would also have lost all other soldiers since he has not fed them.