A can do 50% of a piece of work in 14 days, whereas B can do 60% of the same work in 21 days. A and B work together for 10 days, and C completes the remaining work in 5 days. In how many days can B and C together complete the work?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 10 days
If a part of the work takes some days, the whole work takes days \(\div\) part. Then the work left after 10 days gives C's rate.
A alone: \(\displaystyle 14\div\frac{1}{2}=28\) days; B alone: \(\displaystyle 21\div\frac{3}{5}=35\) days
A and B in 10 days \(\displaystyle =10\left(\frac{1}{28}+\frac{1}{35}\right)=10\times\frac{5+4}{140}=\frac{9}{14}\)
Work left \(\displaystyle =1-\frac{9}{14}=\frac{5}{14}\), done by C in 5 days, so C does \(\frac{1}{14}\) per day
B and C in one day \(\displaystyle =\frac{1}{35}+\frac{1}{14}=\frac{2+5}{70}=\frac{1}{10}\)
B and C together complete the work in 10 days.