A can paint a house in 18 days and B can do it in 12 days. With the help of C, they complete the work in 4 days. How long would C alone take to do the job?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 9 days
People working together add their one-day work. So C's one-day work is the one-day work of all three minus that of A and B.
One-day work of A, B and C together \(\displaystyle =\frac{1}{4}\)
One-day work of A and B \(\displaystyle =\frac{1}{18}+\frac{1}{12}=\frac{2+3}{36}=\frac{5}{36}\)
One-day work of C \(\displaystyle =\frac{1}{4}-\frac{5}{36}=\frac{9-5}{36}=\frac{4}{36}=\frac{1}{9}\)
C alone would take 9 days.