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# A tank can supply water to a village for 40 days. If a leak at the bot

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Joined: 27 May 2013
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A tank can supply water to a village for 40 days. If a leak at the bot  [#permalink]

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21 Aug 2015, 06:17
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85% (hard)

Question Stats:

53% (02:35) correct 47% (02:09) wrong based on 169 sessions

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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.
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Re: A tank can supply water to a village for 40 days. If a leak at the bot  [#permalink]

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21 Aug 2015, 06:26
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rohankant12 wrote:
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.

Loosing 10 liters per day results in a loss of 300 liters in 30 days. So, those 300 liters were for 40 - 30 = 10 days, making daily consumption of the village 300/10 = 30 liters per day. Thus the capacity of the tank is 30*40 = 1200 liters.

Loosing 20 liters plus 30 liters gives 50 liters per day. At this rate the supply will last 1200/50 = 24 days.

Answer: D.
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Re: A tank can supply water to a village for 40 days. If a leak at the bot  [#permalink]

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21 Aug 2015, 06:33
Thanks. the solution was helpful
VP
Joined: 07 Dec 2014
Posts: 1217
A tank can supply water to a village for 40 days. If a leak at the bot  [#permalink]

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20 Dec 2015, 21:51
let w=daily village water usage
40w=30(w+10)
w=30 liters
30 liters x 40 days=1200 liters tank capacity
d=number of days water supply will last with 20 liter daily leak
(20+30)d=1200 liters
d=24 days
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Re: A tank can supply water to a village for 40 days. If a leak at the bot  [#permalink]

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30 Dec 2015, 08:00
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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Re: A tank can supply water to a village for 40 days. If a leak at the bot  [#permalink]

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03 Jan 2016, 07:41
Let X ltr supplied/day
so. 30x ltr supplied and 30.10=300 ltr leaked
total capacity = 300 +30x = 40x [capacity as per expected rate]
x=30
Full capacity=40.30=1200
Secondly,Let , supply lasts for Y days
Full capacity = 30Y[supplied qty]+20Y[Leaked qty]=50y=1200
Hence Y = 24
Ans D
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Re: A tank can supply water to a village for 40 days. If a leak at the bot  [#permalink]

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19 Jul 2017, 01:04
1
rohankant12 wrote:
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.

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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Posts: 1228
Re: A tank can supply water to a village for 40 days. If a leak at the bot  [#permalink]

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19 Jul 2017, 03:09
Bunuel wrote:
rohankant12 wrote:
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.

Loosing 10 liters per day results in a loss of 300 liters in 30 days. So, those 300 liters were for 40 - 30 = 10 days, making daily consumption of the village 300/10 = 30 liters per day. Thus the capacity of the tank is 30*40 = 1200 liters.

Loosing 20 liters plus 30 liters gives 50 liters per day. At this rate the supply will last 1200/50 = 24 days.

Answer: D

hello Bunuel, is my approach correct ?:) if 10 liters * 40 days = 400 liters ,then losing 20 liters = 20 * 40 = 800 liters] 400 = 30 and 800 = x; cross multiply gives 400x=2400, x= 6 ... 30-6 = 24 thank you and have a great day
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Re: A tank can supply water to a village for 40 days. If a leak at the bot  [#permalink]

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25 Jul 2017, 11:04
rohankant12 wrote:
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

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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Re: A tank can supply water to a village for 40 days. If a leak at the bot  [#permalink]

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25 Jul 2017, 12:07
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Per day 10 litres water drain out. It means ,in 30days 300 litres drain out.so if there is no leak problem then remaing 10 days villagers get this 300 litres.it means ,villagers need 30 litres per day.Now we can calculate the capacity of tank which is 30*40=1200. But in 2nd case 20 litres drain out due to leakage it means 50 litres discharge through tank to village per day( 30 litres to village+ 20litres leakage problem) so required days= 1200/50=24 Ans

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Posts: 14
Re: A tank can supply water to a village for 40 days. If a leak at the bot  [#permalink]

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20 Mar 2019, 12:24
rohankant12 wrote:
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.

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.
Re: A tank can supply water to a village for 40 days. If a leak at the bot   [#permalink] 20 Mar 2019, 12:24
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