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: First, we need to find the work done by A and B in one day.
A's one day work = 1/6 B's one day work = 1/8
So, A and B together can complete 1/6 + 1/8 = 7/24 of the work in one day.
Step 2: Now, we know that A, B, and C together completed the work in 3 days. So, they can complete 1/3 of the work in one day.
Step 3: Since we know the work done by A and B in one day, we can find the work done by C in one day by subtracting the work done by A and B from the work done by A, B, and C together.
So, C's one day work = 1/3 - 7/24 = 1/24.
Step 4: Now, we know that the total payment for the work is Rs. 3200. We can find the payment for C by dividing C's one day work by the total work done in one day and multiplying it by the total payment.
So, payment for C = (1/24) / (1/3) * 3200 = Rs. 400.
So, C should be paid Rs. 400.
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