Question

solve the above question

Answer 1

$\large\underline{\sf{Solution-}}$

↝ Let time taken by tap of larger diameter be 'x' hours.

So,

↝ Time taken by tap of smaller diameter be 'x + 10' hours

↝ Let assume that volume of tank be 'y' units.

Now,

Amount of water filled by tap of larger diameter in 1 hour

$\rm \: = \: \dfrac{y}{x}$

Amount of water filled by tap of smaller diameter in 1 hour

$\rm \: = \: \dfrac{y}{x + 10}$

According to statement,

↝ Total time taken is 9 3/8 hours.

So,

$\rm :\longmapsto\:\dfrac{75}{8}\bigg(\dfrac{y}{x} + \dfrac{y}{x + 10} \bigg) = y$

$\rm :\longmapsto\:\dfrac{75y}{8}\bigg(\dfrac{1}{x} + \dfrac{1}{x + 10} \bigg) = y$

$\rm :\longmapsto\:\dfrac{75}{8}\bigg(\dfrac{1}{x} + \dfrac{1}{x + 10} \bigg) = 1$

$\rm :\longmapsto\:\dfrac{1}{x} + \dfrac{1}{x + 10} = \dfrac{8}{75}$

$\rm :\longmapsto\: \dfrac{x + 10 + x}{x(x + 10)} = \dfrac{8}{75}$

$\rm :\longmapsto\: \dfrac{2x + 10}{x(x + 10)} = \dfrac{8}{75}$

$\rm :\longmapsto\: \dfrac{2(x + 5)}{x(x + 10)} = \dfrac{8}{75}$

$\rm :\longmapsto\: \dfrac{x + 5}{x(x + 10)} = \dfrac{4}{75}$

$\rm :\longmapsto\:75x + 375 = 4 {x}^{2} + 40x$

$\rm :\longmapsto\:4 {x}^{2} + 40x - 75x - 375 = 0$

$\rm :\longmapsto\:4 {x}^{2} -35x - 375 = 0$

$\rm :\longmapsto\:4 {x}^{2} -60x + 25x - 375 = 0$

$\rm :\longmapsto\:4x(x - 15) + 25(x - 15) = 0$

$\rm :\longmapsto\:(x - 15)(4x + 25) = 0$

$\bf\implies \:x = 15$

Hence,

↝ Time taken by tap of larger diameter = 15 hours

and

↝ Time taken by tap of smaller diameter = 25 hours