A dam has four inlets ndash A B C and D The dam can be filled in 12 minutes through the first three ...........

Quant (SSC) Pipes&cistern

A dam has four inlets – A, B, C and D. The dam can be filled in 12 minutes through the first three inlets and it can be filled in 15 minutes through the second, the third and fourth inlet also it can be filled through the first and the fourth inlet in 20 minutes. How much time required to fill up the dam by all the four inlets?

10 mins

15 mins

20 mins

25 mins

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Explanation:

(1/A + 1/B + 1/C) = 1/12 …(i)
(1/B + 1/C + 1/D) = 1/15 …(ii)
(1/A + 1/D) = 1/20 …(iii)
From eqn (i) and (ii)
(1/A – 1/D) = 1/60…(iv)
From eqn (iii) and (iv)
A=30 D=60.
Let the time taken to full the tank = T
T(1/A + 1/B +1/C +1/D)= 1
T(1/30 + 1/15) = 1
T = 10 mins