# A water tap fills a tank in p hours and the tap of the bottom of the tank empties it in q hours. If p is less than q and when both the taps are open, the tank is filled in r hours. Then find which of the following is true\begin{align} & a)\dfrac{1}{r}=\dfrac{1}{p}+\dfrac{1}{q} \\ & b)\dfrac{1}{r}=\dfrac{1}{p}-\dfrac{1}{q} \\ & c)\text{ }r=p+q \\ & d)\text{ }r=p-q \\ \end{align}

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Hint: First we will calculate the net tank that is filled in 1 hour and the tank emptied in 1 hour. Hence we will get the net water in the tank after 1 hour. Also we will note that the tank is filled in r hours and hence in 1 hour this net water in the tank will be equal to $\dfrac{1}{r}$

Hence in 1 hour $\dfrac{1}{p}$ part of the tank will be filled.
Hence in 1 hour $\dfrac{1}{q}$ part of the tank will be removed.
Hence in 1 hour the total water in the tank will be $\dfrac{1}{p}-\dfrac{1}{q}$ ………..(1)
Hence, in 1 hour $\dfrac{1}{r}$ tank will be filled. ………….(2)
$\dfrac{1}{r}=\dfrac{1}{p}-\dfrac{1}{q}$