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A and B can compete a piece of work in 18 days. They worked together for 12 days and then A left. B alone finished the work in 15 days. If Rs. 1500 be paid for the work then A's share is:
Answer & Solution
Correct Answer:
Option
C
A and B can complete the work in 18 days, work rate = $$\frac{{100}}{{18}}$$ = 5.55% per day
They together can complete the work in 12 days = 5.55 × 12 = 66.60%
Now, A leaves and B takes another 15 days to complete the whole work, Work rate of B = $$\frac{{33.30}}{{15}}$$ = 2.22% per day
B work for (12 + 15) = 27 days
So, Work done by B in 27 days = 2.22 × 27 ≈ 60% And So 40% work is done by A. so there share should be 60% and 40% ratio.
A's share = 40% of 1500 = Rs. 600
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LoginA + B can do it in 1/18 units/day
so, In 12 days A + B together finish = 12/18 units/day
Remaining work for B to do it alone is = 1 - 12/18 = 6/18 units/day
In the next 15 days B alone does this 6/18 units/day amount of work.
so, in 1 day B does = (6/18 * 1/15) units/day amount of work.
Now B in total works for 27 days.
Total work done by B = 27 * 6/18 * 1/15 units = 3/5 units.
and A does 1 - 3/5 units which is 2/5 units.
hence the share of A is 2/5 * 1500 = Rs 600(Answer)