Test Level 1: Time & Work - 1 - CAT MCQ

Total time taken by A and B together to finish the work = 10 days
And time taken by A alone to finish the work = 15 days
∴ A and B together can do 1/10 of the work in one day and A can do 1/15 of the work in a day.
Work done by B in one day 

So, B takes 30 days to do the work alone. 

Total Work = Number of workers × number of days × number of hours = 20 × 50 × 5 = 5000 units
Let remaining 10 men have to work n hours a day. So, remaining 10 workers work for 35 days.
Total Work = Work done by 20 workers in '15' days working 5 hours a day + Work done by 10 workers in 35 days working n hours a day.
5000 units = 20 × 15 × 5 + 10 × 35 × n
n = 10 hours

The work remains suspended for 4 weeks and 1/2 of 5/6 work done is washed away.
Therefore, they have to do 

By applying chain rule, 


x = 10 week
Therefore, required time = 10 + 4 + 10 = 24 weeks

Since the workers began working one after the other, the interval between their starting times is the same. The first to begin worked five times as long as the last to begin. The number of workers is equal to 5.
If the last worker to begin worked for x hours, then the total working hours = x + 2x + 3x + 4x + 5x = 15x
The men could have finished the work in 6 hours, had they begun at the same time, i.e. 15x = 5 × 6 or x = 2
The job lasted for 5x = 10 hours.

In 8 hours, the outlet pipe can empty 8/10 of the tank.
So, in 8 hours, both the inlet pipes together will fill 18/10 of the tank.
18/10  tank = (2 + 3 litres) × 60 × 8 litres = 2400 litres
Capacity of the tank 

In 1 hour, pipe 'x' can fill 1/8 part of the tank.
In 1 hour, pipe 'y' can empty 1/12 part of the tank.
In 1 hour, both pipes can fill =  part = 1/24 part of the tank.
In 4 hours, both x and y can fill 1/6 part of the tank.
So to fill  5/6th of the tank, tap x will take 5/6 × 8 = 20/3 = 

Let the required time be p hours.
Then, Volume of water flowing through pipe in p hours = Volume of the cistern
⇒ 500 × 10-4 × 8 × 60 × p = 6 × 4 × 4
⇒ p = 4

A needs 160 hours and B needs 240 hours to complete the work separately.

In 1 week, they will work for (2 × 1 + 5 × 4) = 22 hours.
In 4 weeks, they will work for 88 hours.
On Tuesday of the fifth week, they will finish their work.

Work done by P in 10 days 

Remaining work 

Now, 7/8 of work is done by Q in 42 days Whole work will be done by Q in 42 × 8/7 = 48 days
P`s 1 day work = 1/80 and Q`s 1 day work = 1/48

Hence, both will finish the work in 30 days.

Let the amount of work done by 1 man in 1 day be w.
Let the total number of days taken initially to complete the work be d.
Let the amount of total work be W.
So, 60dw = W ...(i)
Now, when 70 men do the work, it takes 8 days less.
So, 70w(d - 8) = W ...(ii)
Equating (i) and (ii), we get:
60d = 70(d - 8)
d = 56
So, W = w × 60 × 56
Now, let 100 men take D days to complete the work.
So, 100 × D × w = W = w × 60 × 56