Two water taps together can fill a tank in

Asked by admin @ 11/08/2021 in Math viewed by 482 People

Two water taps together can fill a tank in 9 3/8 hours.The tap of larger diameter takes 10 hrs less than the smaller one to fill the tank separately.Find the time in which each tap can separately fill the tank.

Answered by admin @ 11/08/2021

Answer :-

→ 25 hours and 15 hours .

Step-by-step explanation :-

→ Let the smaller tap fill the tank in x hours .

→ Then, the larger tap fills it in ( x - 10 ) hours .

→ Time taken by both together to fill the tank = 75/8 hours.

→ Part filled by the smaller tap in 1 hr = 1/x hours .

→ Part filled by the larger tap in 1 hr = 1/( x - 10 ) .

→ Part filled by both the taps in 1 hr = 8/75 .

▶ Now,

$\begin{lgathered}\sf \therefore \frac{1}{x} + \frac{1}{(x - 10)} = \frac{8}{75}. \\ \\ \sf \implies \frac{(x - 10) + x}{x(x - 10)} = \frac{8}{75} . \\ \\ \sf \implies \frac{(2x - 10)}{x(x - 10)} = \frac{8}{75} . \\ \\ \sf \implies75(2x - 10) = 8x(x - 10). \: \: \: \{by \: cross \: multiplication \} \\ \\ \sf \implies150x - 750 = 8 {x}^{2} - 80x. \\ \\ \sf \implies8 {x}^{2} - 230x + 750 = 0. \\ \\ \sf \implies4 {x}^{2} - 115x + 375 = 0. \\ \\ \sf \implies4 {x}^{2} - 100x - 15x + 375 = 0. \\ \\ \sf \implies4x(x - 25) - 15(x - 25) = 0. \\ \\ \sf \implies(x - 25)(4x - 15) = 0. \\ \\ \sf \implies x - 25 = 0. \: \: \green{or} \: \: 4x - 15 = 0. \\ \\ \sf \implies x = 25 \: \: \green{or} \: \: x = \frac{15}{4} . \\ \\ \huge \pink{ \boxed{ \tt \implies x = 25. }} \\ \\ \tt \bigg( \because x = \frac{15}{4} \implies(x - 10) < 0. \bigg)\end{lgathered}$

Hence, the time taken by the smaller tap to fill the tank = 25 hours .

And , the time taken by the larger tap to fill the tank = ( 25 - 10 ) = 15 hours .

Two water taps together can fill a tank in

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