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Two water taps together can fill a tank in $938$ hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

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20, 30

15, 25

25, 20

36, 41

answer is B.

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Detailed Solution

Given
Both taps together fill the tank in

938

hours.

938 = 758

Let the time taken to fill the tank using smaller tap = x hours.
Let the time taken to fill the tank using larger tap

= (x − 10)

hours.
According to the given condition,

1 x + 1 x − 10 = 875

⇒ x − 10 + x x (x − 10) = 875 ⇒ 8 x 2 − 80 x = 150 x − 750 ⇒ 8 x 2 − 230 x + 750 = 0 ⇒ 4 x 2 − 115 x + 375 = 0 ⇒ (x − 25) (4 x − 15) = 0 ⇒ x = 25 or x = 154

But x = 25 because 154 < 10

The smaller tap can fill the tank in 25 hours.
The larger tap can fill the tank

⇒ 25 − 10 ⇒ 15

Hence, the smaller tap can fill in 25 hours and the larger tap can fill the tank in 15 hours and the correct option is 2.

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