Two men undertake to do a piece of work for Rs. 1400. The first man alone can do this work in 7 days while the second man alone can do this work in 8 days. If they working together complete this work in 3 days with the help of a boy, how should the money be divided?OptionsRs. 600, Rs. 550, Rs. 250Rs. 600, Rs. 525, Rs. 275Rs.600, Rs.500, Rs. 300Rs. 500, Rs. 525, Rs.375
Question
Two men undertake to do a piece of work for Rs. 1400. The first man alone can do this work in 7 days while the second man alone can do this work in 8 days. If they working together complete this work in 3 days with the help of a boy, how should the money be divided?OptionsRs. 600, Rs. 550, Rs. 250Rs. 600, Rs. 525, Rs. 275Rs.600, Rs.500, Rs. 300Rs. 500, Rs. 525, Rs.375
Solution
First, let's find out how much work each person can do in a day.
The first man can complete 1/7 of the work in a day. The second man can complete 1/8 of the work in a day.
When they work together with the boy, they can complete 1/3 of the work in a day.
So, the boy can complete 1/3 - 1/7 - 1/8 = 24/168 - 24/168 - 21/168 = 7/168 of the work in a day.
Now, let's find out how much each person should be paid based on the amount of work they can do in a day.
The first man should be paid (1/7) / (1/7 + 1/8 + 7/168) * 1400 = Rs. 600. The second man should be paid (1/8) / (1/7 + 1/8 + 7/168) * 1400 = Rs. 525. The boy should be paid (7/168) / (1/7 + 1/8 + 7/168) * 1400 = Rs. 275.
So, the money should be divided as Rs. 600, Rs. 525, Rs. 275. The correct option is Rs. 600, Rs. 525, Rs. 275.
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