A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C
Question
A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C
Solution
Sure, let's solve this step by step:
Step 1: Find the one day's work of A, B and A+B+C
A's one day's work = 1/6 B's one day's work = 1/8
A and B together can complete the work in 1/(1/6 + 1/8) = 24/7 days
But, A, B and C together completed the work in 3 days.
So, C's one day's work = 1/3 - (1/6 + 1/8) = 1/3 - 7/24 = 1/24
Step 2: Find the share of C
The total amount paid for the work is Rs. 3200.
The share of work done by C is 1/24, while the total work done by A, B and C together is 1/3.
So, the share of C = (C's one day's work / (A's one day's work + B's one day's work + C's one day's work)) * total payment
= (1/24) / (1/3) * 3200 = Rs. 400
So, C should be paid Rs. 400.
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