Question

Three pipes are connected to an inverted cone, with its base at the top. Two inlet pipes, A and B, are connected to the top of the cone and can fill the empty cone in 8 hours and 12 hours, respectively. The outlet pipe C, connected to the bottom, can empty a filled cone in 4 hours. When the cone is completely filled with water, all three pipes are opened. Two of the three pipes remain open for 20 hours continuously and the third pipe remains open for a lesser time. As a result, the height of the

Accepted Answer

C. When height of cone comes down to $50\%$, volume remaining $= (1/2)^3 = 1/8$ of total volume. Volume removed $= 7/8$ of total capacity. Let total capacity $= 24$ liters. Volume to be removed $= \frac{7}{8} 	imes 24 = 21$ liters. Rates: $A = +3	ext{ l/h}$, $B = +2	ext{ l/h}$, $C = -6	ext{ l/h}$. Net rate when all 3 open $= 3 + 2 - 6 = -1	ext{ l/h}$. In 19 hours, $19$ liters removed. To remove total 21 liters, Pipe B staying open for 19 hours 30 minutes satisfies the total drain required.

Pipes and Cisterns Inverted Cone Problem

Explanation

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