Two men undertook to do a job for Rs. 1960. One of them can do it alone in 7 days, and the other in 8 days. With the assistance of a boy they together complete the work in 3 days. How much money will the boy get ?a)Rs. 300b)Rs. 325c)Rs. 385d)Rs. 425Correct answer is option 'C'. Can you explain this answer?

Question

Answer

Let's assume that the amount of work done by the first man in one day is x and the amount of work done by the second man in one day is y.

- The first man can complete the job alone in 7 days, so in one day he completes 1/7th of the work, which can be represented as x = 1/7.
- Similarly, the second man can complete the job alone in 8 days, so in one day he completes 1/8th of the work, which can be represented as y = 1/8.

Combined work:
- When the two men work together, the total work done in one day is x + y.
- With the assistance of the boy, they complete the work in 3 days, which means they complete 1/3rd of the work in one day.
- So, we have the equation x + y + b = 1/3, where b represents the amount of work done by the boy in one day.

Finding the values of x, y, and b:
- We already know that x = 1/7 and y = 1/8.
- Substituting these values in the equation x + y + b = 1/3, we get 1/7 + 1/8 + b = 1/3.
- Finding a common denominator of 56, we get 8/56 + 7/56 + b = 18/56.
- Simplifying the equation, we have 15/56 + b = 18/56.
- Subtracting 15/56 from both sides, we get b = 3/56.

Calculating the boy's share of the money:
- Now that we know the amount of work done by the boy in one day is b = 3/56, we can calculate the boy's share of the money.
- The total amount of work is represented by 1, and the boy does 3/56th of the work.
- So, the boy's share of the money is (3/56) * 1960 = Rs. 105.

Therefore, the boy will receive Rs. 105, which is option C.

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