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Question

Two pipes A and B together fill a cistern in 83 minutes. If A takes 4 minutes more than B, then time taken by A to fill the cistern is .

A
5 minutes
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B
8 minutes
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C
4 minutes
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Solution

The correct option is B 8 minutes
Let pipe B take x minutes to fill the cistern.
Then, the time taken by pipe A to do the same is x+4 minutes.

Portion of the cistern filled by pipe B in one minute =1x, and

portion of the cistern filled by pipe A in one minute =1x+4.

Since the two pipes together fill the cistern in 83 minutes, the portion of the cistern filled in one minute by both pipes together =38.

1x+1x+4=38

x+4+xx(x+4)=38

8×(2x+4)=3x (x+4)

16x+32=3x2+12x

3x24x32=0

3x212x+8x32=0

3x(x4)+8(x4)=0

(3x+8)(x4)=0

x=83 or 4

Since time cannot be negative, we have the time taken by pipe B to fill the cistern is x=4 minutes.

Thus, the time taken by pipe A to fill the cistern is x+4=4+4=8 minutes.

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