There are two taps to fill a tank while a thi | vedclass

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Question

(C) Let the capacity of the tank be $1$ unit.The rate of the first tap is $\frac{1}{10}$ tank per minute.The rate of the second tap is $\frac{1}{12}$

Vedclass · Accepted Answer

$8 	ext{ minutes and } 34 	ext{ seconds}$

Vedclass · Answer

(C) Let the capacity of the tank be $1$ unit.The rate of the first tap is $\frac{1}{10}$ tank per minute.The rate of the second tap is $\frac{1}{12}$ tank per minute.Let the rate of the third tap (emptying) be $x$ tank per minute.When all three taps are open,the net rate is $\frac{1}{15}$ tank per minute.Therefore,$\frac{1}{10} + \frac{1}{12} - x = \frac{1}{15}$.Calculating the sum: $\frac{6+5}{60} - x = \frac{1}{15} \implies \frac{11}{60} - x = \frac{4}{60}$.Thus,$x = \frac{11}{60} - \frac{4}{60} = \frac{7}{60}$ tank per minute.The time taken by the third tap to empty the full tank is $\frac{1}{x} = \frac{60}{7}$ minutes.$\frac{60}{7} 	ext{ minutes} = 8 \frac{4}{7} 	ext{ minutes} \approx 8 	ext{ minutes and } 34 	ext{ seconds}$.

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