8. Two water taps together can fill a tank 9 in hours. The tap of larger diameter takes 10 hours less
8
than the smaller one to fill the tank separately. Then the time in which larger diameter tap can
separately fill the tank, is
( 16 hours
(d) 20 hours
25 han
(c) 10 hours
Answers
Explanation:
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 .
Answer:
Hii Branlist Hope It Helps You
Explanation:
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,
$$\begin{lgathered}\begin{lgathered}\sf \therefore \frac{1}{x} + \frac{1}{(x - 10)} = \frac{8}{75}. \\ \\ \sf \implies \frac{(x - 10) + x}{x(x - 10)} = \frac{8}{75} . \\ \\ \sf \implies \frac{(2x - 10)}{x(x - 10)} = \frac{8}{75} . \\ \\ \sf \implies75(2x - 10) = 8x(x - 10). \: \: \: \{by \: cross \: multiplication \} \\ \\ \sf \implies150x - 750 = 8 {x}^{2} - 80x. \\ \\ \sf \implies8 {x}^{2} - 230x + 750 = 0. \\ \\ \sf \implies4 {x}^{2} - 115x + 375 = 0. \\ \\ \sf \implies4 {x}^{2} - 100x - 15x + 375 = 0. \\ \\ \sf \implies4x(x - 25) - 15(x - 25) = 0. \\ \\ \sf \implies(x - 25)(4x - 15) = 0. \\ \\ \sf \implies x - 25 = 0. \: \: \green{or} \: \: 4x - 15 = 0. \\ \\ \sf \implies x = 25 \: \: \green{or} \: \: x = \frac{15}{4} . \\ \\ \huge \pink{ \boxed{ \tt \implies x = 25. }} \\ \\ \tt \bigg( \because x = \frac{15}{4} \implies(x - 10) < 0. \bigg)\end{lgathered}\end{lgathered}$$
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 .