CAT 2018 Question Paper Shift 2 Solved Paper

Question : 73 of 100

Marks: +1, -0

A tank is emptied everyday at a fixed time point. Immediately thereafter, either pump A or pump B or both start working until the tank is full. On Monday, A alone completed filling the tank at 8 pm. On Tuesday, B alone completed filling the tank at 6 pm. On Wednesday, A alone worked till 5 pm, and then B worked alone from 5 pm to 7 pm, to fill the tank. At what time was the tank filled on Thursday if both pumps were used simultaneously all along?
Options

4:36 pm
4:12 pm
4:48 pm
4:24 pm

Validate

Solution:

Let

x

be the time, on a 24 hours clock, at which the tank is empty.
Time taken by pipe

A

alone to fill the tank is

(20-x)

hrs.
Time taken by pipe

{B}

alone to fill the tank is

(18- {x})

hrs.
On the other day, A fill the tank for

(15- {x})

hrs and

{B}

for

2 {hrs}

.
Let

A

and

B

be the rate of works of pipe

A

and

B

respectively.

⇒(20-x) A=(18-x) B=(17-x) A+2 B

⇒ \;{A}/{B}=\;{2}/{3}

⇒(20-x) 2=(18-x) 3

⇒(20-x) A=1

Let

(20-x) A=1

A=\;{1}/{6}

B=\;{1}/{4}

When both work simultaneously, time taken

=\;{1}/{{1}/{6}+\;{1}/{4}}=2.4 {hrs}=2 {hrs} 24 {min}

The tank will be filled by 16: 24i.e..4:

24 {pm}

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