A pipe fills \(\displaystyle\frac{2}{5}\) of an empty tank in 6 minutes. In how many more minutes will it fill the rest of the tank?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 9
The pipe fills the tank at a steady rate, so the time taken is proportional to the part filled.
\(\displaystyle \text{Time for the whole tank} = 6 \div \frac{2}{5} = 15 \text{ minutes}\)
\(\text{Time for the rest} = 15 - 6 = 9 \text{ minutes}\)
So the pipe needs 9 more minutes to fill the remaining \(\frac{3}{5}\) of the tank.
Why the other options are incorrect
Option (1) 15 — Incorrect. 15 minutes is the time for the whole tank; 6 of those minutes have already passed.
Option (2) 6 — Incorrect. In 6 minutes the pipe fills only another \(\frac{2}{5}\), but \(\frac{3}{5}\) of the tank is still empty.
Option (3) 10 — Incorrect. In 10 minutes the pipe fills \(\frac{10}{15} = \frac{2}{3}\) of the tank, which is more than the \(\frac{3}{5}\) that is left.