Aptitude - Chain Rule - Discussion

3 pumps working 8 hours.
So total hours = 3 * 8 = 24 * 2 = 48 to fill.
So can empty 48/4 = 12 hours.
Then, the answer = 12.

Let pumps - 'p', no.of hrs/day - 'h', no.of days - 'd'.

For this type of problems, first know what we have to find? here we have to find hrs/day i.e. 'h'.

Now, find out the relation of 'h' with other parameters 'p' and 'd'.

If no.of pumps increases, no.of hrs/day decreases (inverse proportion).

p & (1/h). (1) **Assume &-proportionality symbol**.

If no.of days increases, no.of hrs/day decreases (inverse proportion).

d & (1/h). (2).

From (1) & (2).

pd & (1/h). (3).

=> pdh=constant.

=> p1*d1*h1=p2*d2*h2.

=> 3*2*8=4*1*x.

=> x=12.

3 pumps = 8 hrs/day.

1 pump = 8*3 = 24 hrs/day and 48 hrs in 2 days.

Considering 1 day work of 3 pumps we know that 24/3 = 8.

Now f we consider 1 day work of 4 pumps should not it be 24/4 = 6.

Please anyone, why? are we considering for two days when it is asked for 1 day work?

Maths Master Really Explained It Well. I Need More Of Your Teaching.

3 pumb work in 2 days = 16 hours for empty the tank
1 pump work in 2 days = 16*3 = 48 hours for empty the tank
so 4 pump ...........= (16*3)/4 = 12..

I like @Mehar's Method. So simple to understand. Thanks.

@Math master: I didn't get your first statement.

If 3 pumps work for 8 hours than total hours in 1 day is 3 * 8 = 24 hours.

So in 2 days total hours of work is 48 hours.

So for 4 pumps the work distributed is (48 / 4) = 12 hours.

Math master's solution is great.

3*8 = 24 hours in 2 day i.e., 12 hours a day with 3 pumps.

How can it be 12 hours with 4 pumps?