Question

solve this ques.. please ans step by step..

Answer 1

Let the smaller tap takes x hours to fill the tank.
In 1 hour, smaller tap will fill = 1/x part of tank

Larger tap will take = (x-10) hours to fill it.
In 1 hour, larger tap will fill = 1/(x-10) part of tank

In 1 hour, both will fill = [1/x + 1/(x-10) ] part of tank

it is given that both tap can fill the tank in 9 3/8 hours = 75/8 hours

Thus
$\frac{75}{8} \times ( \frac{1}{x} + \frac{1}{x - 10} ) = 1 \\ \\ \frac{75}{8} \times \frac{(x - 10) +(x)}{x(x - 10)} = 1$

$\frac{75}{8} \times \frac{2x - 10}{ {x}^{2} - 10x} = 1 \\ \\ 75(2x - 10) = 8( {x}^{2} - 10x)$

$150x - 750 = 8 {x}^{2} - 80x \\ \\ 8 {x}^{2} - 80x - 150x + 750 = 0$

$8 {x}^{2} - 230x + 750 = 0$

This is the required quadratic equation.