A alone can do a piece of work in 30 days, while B alone can do it in 15 days and C alone can do it in 10 days. If in every second day B and in every third day C help A in doing the work, how many days still be required to complete the whole work? (work and time)

Shohan

8 views

2025-01-04 04:42

1 Answers

Shohan

LCM of 2 and 3 is 6

Work done in first 6 days = $(\frac{6}{30} + \frac{3}{15} + \frac{2}{10}) = \frac{6 + 6 + 6}{30} = \frac{18}{30} = \frac{4}{15}$

Remaining work = $(1 - \frac{3}{5}) = (\frac{5 - 3}{5}) = \frac{2}{5}$

Next 3 days work done by them= $(\frac{3}{30} + \frac{1}{15} + \frac{1}{10}) = \frac{3 + 2 + 3}{30} = \frac{8}{30} = \frac{4}{15}$

Remaining work after 9 days = $(\frac{2}{5} - \frac{4}{15}) = (\frac{6 - 4}{15}) = \frac{2}{15}$

In 10^th days, B will help A, thus work done by them after 9 days= $(\frac{1}{30} + \frac{1}{15}) = \frac{1 + 2}{30} = \frac{3}{30} = \frac{1}{10}$

Remaining work= $(\frac{2}{15} - \frac{1}{10}) = (\frac{4 - 3}{30}) = \frac{1}{30}$

In 11^th days, A alone can do $\frac{1}{3}$ part of work which is the amount of remaining work.

Total 11 days will be required to complete the whole work. ans.

8 views Answered 2024-12-14 13:31

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