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A can do a certain work in 12 days and B...

A can do a certain work in 12 days and B can do it in 18 days. They worked together for 4 days. The remaining work was completed by C alone in 6 days. If they get Rs 3.240 for the whole work, then the share of C in this amount will be:

A

Rs 1,080

B

Rs 1,440

C

Rs 1,260

D

Rs 1,170

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, we can follow these calculations: ### Step 1: Calculate the work done by A and B in one day. - A can complete the work in 12 days, so A's work in one day = \( \frac{1}{12} \) of the work. - B can complete the work in 18 days, so B's work in one day = \( \frac{1}{18} \) of the work. ### Step 2: Find the combined work done by A and B in one day. - Combined work of A and B in one day = \( \frac{1}{12} + \frac{1}{18} \). - To add these fractions, find a common denominator. The least common multiple of 12 and 18 is 36. - Convert the fractions: - \( \frac{1}{12} = \frac{3}{36} \) - \( \frac{1}{18} = \frac{2}{36} \) - Therefore, combined work = \( \frac{3}{36} + \frac{2}{36} = \frac{5}{36} \). ### Step 3: Calculate the total work done by A and B in 4 days. - Work done by A and B in 4 days = \( 4 \times \frac{5}{36} = \frac{20}{36} = \frac{5}{9} \) of the work. ### Step 4: Calculate the remaining work. - Total work = 1 (whole work). - Remaining work = \( 1 - \frac{5}{9} = \frac{4}{9} \) of the work. ### Step 5: Calculate the work done by C. - C completes the remaining \( \frac{4}{9} \) of the work in 6 days. - Therefore, C's work in one day = \( \frac{4/9}{6} = \frac{4}{54} = \frac{2}{27} \) of the work. ### Step 6: Calculate the total amount and C's share. - Total payment for the work = Rs. 3240. - The total work can be considered as 1 unit of work, and the payment can be divided based on the amount of work done. - Work done by C = \( \frac{4}{9} \). - Total work done = 1 unit (A + B + C). - C's share = \( \frac{C's \ work}{Total \ work} \times Total \ payment \). - C's share = \( \frac{4/9}{1} \times 3240 = \frac{4 \times 3240}{9} = 1440 \). ### Final Answer: C's share in the amount will be Rs. 1440. ---
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