Two inlet pipes can fill a cistern in 10 hour | vedclass

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(C) Let the capacity of the tank be $C$ $gallons$.Rate of the first inlet pipe $= \frac{C}{10}$ $gallons/hour$.Rate of the second inlet pipe $= \frac{

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$600$

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(C) Let the capacity of the tank be $C$ $gallons$.Rate of the first inlet pipe $= \frac{C}{10}$ $gallons/hour$.Rate of the second inlet pipe $= \frac{C}{12}$ $gallons/hour$.Rate of the outlet pipe $= -80$ $gallons/hour$.When all three pipes work together,the net rate is $\frac{C}{20}$ $gallons/hour$.Therefore,$\frac{C}{10} + \frac{C}{12} - 80 = \frac{C}{20}$.Rearranging the terms: $\frac{C}{10} + \frac{C}{12} - \frac{C}{20} = 80$.Taking the least common multiple $(LCM)$ of $10, 12, 20$,which is $60$:$\frac{6C + 5C - 3C}{60} = 80$.$\frac{8C}{60} = 80$.$\frac{2C}{15} = 80$.$C = 80 	imes \frac{15}{2} = 600$.Thus,the capacity of the tank is $600$ $gallons$.

Two inlet pipes can fill a cistern in $10$ $hours$ and $12$ $hours$ respectively,and an outlet pipe can empty $80$ $gallons$ of water per hour. All three pipes working together can fill the empty cistern in $20$ $hours$. What is the capacity (in $gallons$) of the tank?

Similar Questions

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