Two taps, P and Q, can fill an empty water drum in 24 minutes and 40 minutes respectively. The drum is empty and both taps are turned on together. After how many minutes will the drum be two-thirds full?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 10 minutes
Take the capacity of the drum as the LCM of 24 and 40, that is 120 units. Taps running together add the units they fill each minute.
Tap P: \(120\div24=5\) units per minute
Tap Q: \(120\div40=3\) units per minute
Both together: \(5+3=8\) units per minute
Two-thirds of the drum \(\displaystyle=\frac{2}{3}\times120=80\) units
Time \(=80\div8=10\) minutes
The drum is two-thirds full after 10 minutes.