Question

Two pipes together can fill a tank in 12 hour. If first pipe can fill the tank in 10hours.faster than the second, then how many hours Will the second pipe take to fill the tank

Answer 1

Step-by-step explanation:

Time required to fill the tank by second pipe => x hours

Time required to fill the tank by first pipe =>

(x-10) hours

Two pipes together can fill a tank in 12 hours.

$\frac{1}{x} + \frac{1}{(x - 10)} = \frac{1}{12} = > \frac{2x - 10}{x(x - 10)} = \frac{1}{12} = >$

$12(2x - 10) = x(x - 10) = >$

${x}^{2} - 10x = 24x - 120 = > {x}^{2} - 34x$

$+ 120 = 0 = > {x}^{2} - 4x - 30x + 120 =$

$0 = > {x}^{2} - 30x - 4x + 120 = 0 = >$

$x(x -4) - 30( x - 4) = 0 = >$

$(x - 4)(x - 30) = 0 = > x = 4 \: or \: 30$

So x can't be 4 as (x-10 ) needs to be +ve

Hence x is 30 hours. The second pipe takes 30 hours to fill the tank.

Answer 2

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