A and B can do a piece of work in 12 days. B and C together can do it in 15 days. If A is twice as good a workman as C, find the number of days in which B alone can do the work?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 20 days
A person who finishes a job in \(n\) days does \(\frac{1}{n}\) of it in one day, and the one-day work of people working together is added. “A is twice as good a workman as C” means A does twice C’s work in a day.
The one-day work given (A, B, C stand for one day’s work):
\(\displaystyle A+B=\frac{1}{12}\) (1)
\(\displaystyle B+C=\frac{1}{15}\) (2)
\(A=2C\) (3)
Finding C (subtracting (2) from (1), B cancels):
\(\displaystyle A-C=\frac{1}{12}-\frac{1}{15}=\frac{5-4}{60}=\frac{1}{60}\)
By (3), \(A-C=2C-C=C\), so \(\displaystyle C=\frac{1}{60}\)
Finding B (from (2)):
\(\displaystyle B=\frac{1}{15}-\frac{1}{60}=\frac{4-1}{60}=\frac{3}{60}=\frac{1}{20}\)
B does \(\frac{1}{20}\) of the work a day, so B alone needs 20 days