Two taps, P and Q, can fill an empty water drum in 36 minutes and 45 minutes respectively. The drum is empty and both taps are turned on together. After how many minutes will the drum be three-quarters full?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 15 minutes
Take the capacity of the drum as the LCM of 36 and 45, that is 180 units. Taps running together add the units they fill each minute.
Tap P: \(180\div36=5\) units per minute
Tap Q: \(180\div45=4\) units per minute
Both together: \(5+4=9\) units per minute
Three-quarters of the drum \(\displaystyle=\frac{3}{4}\times180=135\) units
Time \(=135\div9=15\) minutes
The drum is three-quarters full after 15 minutes.