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CAT 2018 [SLOT 2] Quant Question with Solution 12

Question:
A water tank has inlets of two types A and B. All inlets of type A when open, bring in water at the same rate. All inlets of type B, when open, bring in water at the same rate. The empty tank is completely filled in 30 minutes if 10 inlets of type A and 45 inlets of type B are open, and in 1 hour if 8 inlets of type A and 18 inlets of type B are open. In how many minutes will the empty tank get completely filled if 7 inlets of type A and 27 inlets of type B are open?

Show Answer
Correct Answer: 48
Let the rate of filling of Type A and Type B pipes be a and b respectively.
Given 30×(10a + 45b) = 1 and 60×(8a + 18b) = 1
=> 30 × (10a + 45b) = 60 × (8a + 18b)
=> 10a + 45b = 16a + 36b
=> 3b = 2a or a = 1.5b
The total work = 30 × (10a + 45b) = 30 × (15b + 45b)
= 1800b
Required answer $=\frac{1800 b}{7 a+27 b}=\frac{1800 b}{10.5 b+27 b}=48$

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