Question

A tyre has two punctures. The first puncture alone would have made the tyre flat in $9$ minutes and the second alone would have done it in $6$ minutes. If air leaks out at a constant rate how long does it take both the punctures together to make it flat ?

• A. $1\frac{1}{2}$ minutes
• B. $3\frac{1}{2}$ minutes
• C. $3\frac{3}{5}$ minutes
• D. $4\frac{1}{4}$ minutes

Answer 1

The correct option is C $3\frac{3}{5}$ minutes

In 1 minute, first puncture can make $\frac{1}{9}th$ of the tyre flat.

In 1 minute, second puncture can make $\frac{1}{6}th$ of the tyre flat.

Together, in 1 minute, both punctures can make $\frac{1}{9}+\frac{1}{6}=\frac{15}{54}th$ of the tyre flat.

So, time taken for both the punctures to make the tyre flat is $\frac{54}{15}minutes=\frac{18}{5}=3\frac{3}{5}minutes$