Latest Book Aptitude Question SOLUTION: Two water taps together fill a tank in 9 3/8 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

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(#M40009607) BOOK question Keep an EYE

Two water taps together fill a tank in 9 3/8 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.

Asked In Book Devendra Marghade (12 years ago)

Solved Vignesh Read Solution (1)

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Vignesh  (12 years ago)

Larger tap fill in = 15hrs
Smaller tap fill in = 25hrs

Let x = No. of hours required to fill by longer tap.
So, x+10 = No. of hours required to fill by smaller tap.
And v = Volume of the tank.

Portion of tank fill in 1hr by longer tap = v/x
Portion of tank fill in 1hr by smaller tap = v/x+10
Portion of tank fill in 1hr by both tap = v/(75/8)

v/x + v/(x+10) = v/(75/8)

1/x + 1/(x+10) = 8/75

75(2x+10) = 8(x^2 +10x)
150x+750 = 8x^2 + 80x
8x^2 - 150x + 80x -750 = 0
8x^2 - 70x - 750 = 0
By simplifying,
4x^2 - 35x - 375 = 0

(i.e) b^2 -4ac = 7225>0
x = 35+(square root (7225)) /8 (or) x = 35 - (square root (7225)) /8
x = (35+85) /8
x = 120/8
[x = 15hrs] and [x+10 = 15+10 = 25hrs].

Therefore,

Larger tap can fill in = 15hrs
Smaller tap can fill in= 25hrs

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