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 dore 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?
Answer & explanation
Correct answer: option 4
According to question ,
The first puncture alone would have made the tyre flat in 9 minutes
So , In 1 minute, the first puncture can make \(\frac{1}{9}\)th of the tyre
The second puncture alone would have made the tyre flat in 18 minutes
So , the second puncture can make \(\frac{1}{18}\)th of the tyre flat In 1 minute
The third puncture alone would have made the tyre flat in 6 minutes
So , In 1 minute, the third puncture can make \(\frac{1}{6}\)th of the tyre flat
In 1 minute, the all tyres can make \(\frac{1}{9}\) + \(\frac{1}{18}\) + \(\frac{1}{6}\) = \(\frac{1}{3}\) of the tyre flat
Total required time to flat = 3 minutes
Hence , All punctures can make the tyre flat in 3 minutes