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

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Solution

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

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

(A+B)'s 1-day work = 115 (A+B)'s 6-day work = 615 Remaining work = 1 - 615 = 915 = 35 A takes 30 days to complete remaining work. A's 1-day work = 3530 = 150 So, A takes 50 days to complete full work alone. B's 1-day work = 115 - 150 = 7150 B takes 1507 or 21.4 or 21 days (approx.)