Question

X and Y together need to complete a piece of work in 15 days. They both start working together, but after 6 days Y falls ill, so X takes 30 more days to complete the work alone. How long will Y take to complete the work alone?
(3 marks)

Answer 1

(X+Y)'s 1-day work = $\frac{1}{15}$
(X+Y)'s 6-day work = $\frac{6}{15}$
Remaining work = 1 - $\frac{6}{15}$ = $\frac{9}{15}$ = $\frac{3}{5}$ (1 mark)
X takes 30 days to complete remaining work.
X's 1-day work = $\frac{\frac{3}{5}}{30}$ = $\frac{1}{50}$
So, X takes 50 days to complete full work alone.
(1 mark)
Y's 1-day work = $\frac{1}{15}$ - $\frac{1}{50}$ = $\frac{7}{150}$
Y takes $\frac{150}{7}$ or 21.4 or 21 days (approx.)
(1 mark)