CAT 2018 Question Paper Shift 2 Solved Paper

Question : 86 of 100

Marks: +1, -0

A water tank has inlets of two types A and B. All inlets of type A when open, bring in water atthe same rate. All inlets of type B, when open, bring in water at the same rate. The empty tankis completely filled in 30 minutes if 10 inlets of type A and 45 inlets of type B are open, and in1 hour if 8 inlets of type A and 18 inlets of type B are open. In how many minutes will theempty tank get completely filled if 7 inlets of type A and 27 inlets of type B are open?

Your Answer:

Validate

Solution:

Let the rate of filling of Type A and Type B pipes be a and b respectively.
Given

30 ×(10 {a}+45 {b})=1

and

60 ×(8 {a}+18 {b})=1

⇒30 ×(10 {a}+45 {b})=60 ×(8 {a}+18 {b})

⇒ 10 {a}+45 {b}=16 {a}+36 {b}

⇒ 3 {b}=2 {a}

{a}=1.5 {b}

The total work

=30 ×(10 {a}+45 {b})=30 ×(15 {b}+45 {b})

=1800 {b}

Required answer

=\;{1800 b}/{7 a+27 b}=\;{1800 b}/{10.5 b+27 b}=48

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