A tyre has 3 punctures The first puncture alone would have made the tyre flat in 9 minutes the secon...........

Quantitative Aptitude (CGL) Time and work

A tyre has 3 punctures. The first puncture alone would have made the tyre flat in 9 minutes, the second alone would have done

it in 18 minutes, the third alone would have done it in 6 minutes. If the air leaks out at a constant rate, then how long (in

minutes) does it take for

all the punctures together to make it flat ?

This questions was previously asked in

SSC CGL 13th April 2022 Shift-2

- Time taken by each puncture alone to make the tyre flat:

- First puncture: 9 minutes.

- Second puncture: 18 minutes.

- Third puncture: 6 minutes.

- Rate of air leaking for each puncture:

- Rate for first puncture: 1/9 of the tyre per minute.

- Rate for second puncture: 1/18 of the tyre per minute.

- Rate for third puncture: 1/6 of the tyre per minute.

- Combined rate of all punctures:

\frac{1}{9} + \frac{1}{18} + \frac{1}{6} = \frac{2}{18} + \frac{1}{18} + \frac{3}{18} = \frac{6}{18} = \frac{1}{3}

- Time taken for all punctures together:

\text{Time} = \frac{1 \text{ tyre}}{1/3 \text{ of the tyre/minute}} = 3 \text{ minutes}

- Correct option is: Option 3: 3

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