P can complete a work in 20 days while Q is 25% more efficient than P. Q worked for 6 days and left, remaining work is completed by R in 15 days. Find in how many days R can complete the whole work alone?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 24 days
One day’s work is the fraction of the whole work finished in one day. A worker who is 25% more efficient does 1.25 times as much work each day.
P’s one day’s work \(\displaystyle =\frac{1}{20}\)
Q’s one day’s work \(\displaystyle =1.25\times\frac{1}{20}=\frac{1}{16}\)
Work done by Q in 6 days \(\displaystyle =\frac{6}{16}=\frac{3}{8}\)
Work left for R \(\displaystyle =1-\frac{3}{8}=\frac{5}{8}\)
R does \(\frac{5}{8}\) of the work in 15 days, so R alone does the whole work in \(\displaystyle 15\times\frac{8}{5}=24\) days