CAT 2018 Question Paper Shift 1 Solved Paper

Question : 97 of 100

Marks: +1, -0

A tank is fitted with pipes, some filling it and the rest draining it. All filling pipes fill at thesame rate, and all draining pipes drain at the same rate. The empty tank gets completely filledin 6 hours when 6 filling and 5 draining pipes are on, but this time becomes 60 hours when 5filling and 6 draining pipes are on. In how many hours will the empty tank get completely filledwhen one draining and two filling pipes are on?

Your Answer:

Validate

Solution:

Let the rate of each filling pipes be 'x

1{\ts} {/} {\hr}

' similarly, the rate of each draining pipes be 'y

{\lts}{/} {\hr}

'.
As per the first condition,
Capacity of tank

=(6 {x}-5 {y}) × 6 . . . . . . . . . .( {i})

Similarly, from the second condition,
Capacity of tank

=(5 {x}-6 {y}) × 60 . . . . . .

(ii)
On equating (i) and (ii), we get

(6 x-5 y) × 6=(5 x-6 y) × 60

or,

6 x-5 y=50 x-60 y

or,

44 x=55 y

or,

4 {x}=5 {y}

or,

x=1.25 y

Therefore, the capacity of the tank

=(6 x-5 y) × 6=(7.5 y-5 y) × 6=15 y

lts
Effective rate of 2 filling pipes and 1 draining pipe

=(2 x-y)=(2.5 y-y)=1.5 y

Hence, the required time

=15 {y}{/}1.5 {y}=10

hours.

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