Select the correct answerA and B together can do a piece of work in 12 days which B and C together do in 16 days. If A works for 5 days, B works for 7 days than C completes the remaining work in 13 days. In how much time B alone does the whole work?Options24 days48 days16 days12 days
Question
Select the correct answerA and B together can do a piece of work in 12 days which B and C together do in 16 days. If A works for 5 days, B works for 7 days than C completes the remaining work in 13 days. In how much time B alone does the whole work?Options24 days48 days16 days12 days
Solution
To solve this problem, we need to first find the rates at which A, B, and C work.
- A and B together can do the work in 12 days. So, their combined rate is 1/12 work per day.
- B and C together can do the work in 16 days. So, their combined rate is 1/16 work per day.
Now, we know that A works for 5 days, B works for 7 days, and C works for 13 days to complete the work. This means that:
- A does 5*(1/12 - 1/16) = 5/48 of the work.
- C does 13*(1/16 - 1/12) = 13/48 of the work.
Since the total work is 1, B must do the remaining 1 - 5/48 - 13/48 = 30/48 = 5/8 of the work.
If B can do 5/8 of the work in 7 days, then to do the whole work, B would need 7/(5/8) = 56/5 = 11.2 days.
However, this is not one of the options given. There might be a mistake in the problem or in the options provided.
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