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Nikhil Manohar

· started a discussion

· 1 Months ago

solution (Question: 112232.0 )

No of litres poured in 12 hrs = 6x60x12
This extra pouring elongated time from 8 hrs to 12 hrs.
So capacity = 6*60*12÷4*8
= 8640

Question:
A cistern has a leak which would empty it in 8 hours. If a tap is turned on which admits 6 litres of water a minutes into the cistern then leak empty the tank in 12 hours, find capacity of cistern.
Options:
A) 9000 litres
B) 8640 litres
C) 10000 litres
D) 4500 litres
Solution:
Ans: (b)

Suppose tap can fill the tank in x hours

Leak’s 1 hr emptying capacity =\(\cfrac{1}{8}\)  

Tap’s 1 hr filling capacity  = \(\cfrac{1}{x}\)

When the tap is on,

Leak’s 1 hr emptying capacity = \(\cfrac{1}{8}-\cfrac{1}{x}=\cfrac{x-8}{8x}\)

\(\therefore\) Tank would empty in \(\cfrac{8x}{x-8}\) hours

\(\cfrac{8x}{x-8}\)  = 12

or 8x = 12x - 96   or    4x = 96

\(\therefore\)  x = 24 hours.

Since cistern pours 6 litres in 1 minute

\(\therefore\) cistern’s capacity = 6 \(\times\) 24 \(\times\) 60 = 8640 litres

rakesh kumar

· commented

· 1 Months ago

excellent bro thnx

vineet

· commented

· 1 Months ago

Thanks
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