Question

Three ducts M, N and P can fill a tank in 18 hours. After working at it together for 6 hours, P is closed and M and N can fill the remaining part in 21 hours. The number of hours taken by P alone to fill the reservoir is:

• A. 105 hrs
• B. 84 hrs
• C. 42 hrs
• D. 78 hrs
• E. None of these

Answer 1

The correct option is C

42 hrs

$\text{M+ N + P =}\frac{1}{18}\text{For 6 hours=}6\times \frac{1}{18}\text{=}\frac{1}{3}\text{Remaining =}\frac{2}{3}\text{(M + N)'s 21 hours work =}\frac{2}{3}\text{(M + N)'s 1 hours work =}\frac{1}{21}\times \frac{2}{3}=\frac{2}{63}\text{P's 1 hour work = (M + N + P)'s work - (M + N)'s work =}\frac{1}{18}-\frac{2}{63}=\frac{1}{42}\text{P alone can fill the tank in 42 hours.}$