A tank can supply water to a village for 40 days. If a leak at the bottom of the tank drains out 10 litres per day, the supply lasts for 30 days only. For how many days will the supply last if the leak drains out 20 litres per day?

A) 15
B) 18
C) 20
D) 24
E) 32

Can some one help me with this question.

Thanks. the solution was helpful

For this problem, we could also take an intuitive approach and avoid calculations.

We know that the water tank usually lasts 40 days, but with a leak of 10 litres/day it will last only 30 days.

That means that 30 days of leaking loses 10 days worth of water for the village. Now if the leak is doubled to 20 litres/day, 30 days of leaking would lose 20 days of water for the village. But the supply would now last less than 30 days (since the tank is losing more water each day). So the amount of water lost must be less than 20 days worth.

Therefore, the amount of water lost must be between 10 and 20 days worth, so the water tank will last the village somewhere between 20 and 30 days.

Looking at the answer choices, only one option is between 20 and 30 days. Answer D, 24 days.

Note that this approach only works because there is only one answer choice between 20 and 30. If the answer choices included multiple answers between 20 and 30 (e.g. 22, 24, 25), then you would need to do the calculations to determine the correct answer.

It is important on the GMAT to have a good intuitive feel for problems. It doesn't mean you'll be able to find every answer without doing any calculations, but it can help to narrow down answer choices if you know the answer must be in a certain range or of a magnitude. It is always good to think about the problems beyond the numbers to get a good understanding of what is going on.
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Let the water supplied per day be y.
Let x be the total volume of water in tank.

so x/y = 40
x = 40y

Also, (x-30*10)/y = 30
40y = 30y +300
10y = 300
y = 30 litres/day

x = 40 * 30 = 1200 litres

If 20 litres/day of water is drained out from tank. Let z be the number of days the supply will last.
(1200 - 20z)/y = z
(1200 - 20z)/30 = z
1200 = 50 z
z = 24 days

Answer D
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We can let x = the number of litres of water the village uses per day. Since the tank can supply water to the village for 40 days, the tanks holds 40x litres of water (if there is no leak).

We are given that if there is a leak at the bottom of the tank that drains out 10 litres per day, the supply lasts for 30 days only. Thus, we can create the following equation:

40x - 30(10) = 30x

10x = 300

x = 30

Thus, we know the village uses 30 litres of water a day and the tank holds 40(30) = 1200 litres of water (if there is no leak).

We are asked to determine the number of days the supply will last if the leak drains out 20 litres per day. If we let n = the number of days the supply will last if the leak drains out 20 litres per day, we can create the following equation:

1200 - 20n = 30n

1200 = 50n

n = 24

Answer: D
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With 10l/day loss,
no. of days lost /no. of days supply lasts= 10/30=1/3
With 20l/day loss,
no. of days lost/ no. of days supply lasts=x
Forming an equation using the info,
10/(1/3)=20/x
ie., 3x=2
& x=2/3

Therefore, no. of days supply lasts= 40*(3/5)
=24.