elect the correct answerA can do a piece of work in 90 days, B in 40 days and C in 12 days. They work for a day each in turn i.e., first day A does it alone, B does it the second day and C the third day. After that A does it for another day, and so on. After finishing the work they get Rs. 240. If the wages are divided in proportion to the work done by them, find what each will getOptionsA Rs.22, B Rs.50 and C Rs. 132A Rs. 24, B Rs.54 and C Rs. 162A Rs. 26, B Rs.52 and C Rs. 142A Rs. 20, B Rs. 44 and C Rs.182
Question
elect the correct answerA can do a piece of work in 90 days, B in 40 days and C in 12 days. They work for a day each in turn i.e., first day A does it alone, B does it the second day and C the third day. After that A does it for another day, and so on. After finishing the work they get Rs. 240. If the wages are divided in proportion to the work done by them, find what each will getOptionsA Rs.22, B Rs.50 and C Rs. 132A Rs. 24, B Rs.54 and C Rs. 162A Rs. 26, B Rs.52 and C Rs. 142A Rs. 20, B Rs. 44 and C Rs.182
Solution
To solve this problem, we first need to find out how much work each person does in a day.
- A can complete the work in 90 days, so in one day, A does 1/90 of the work.
- B can complete the work in 40 days, so in one day, B does 1/40 of the work.
- C can complete the work in 12 days, so in one day, C does 1/12 of the work.
Now, they work in turns. So, in 3 days, the total work done by A, B, and C is (1/90 + 1/40 + 1/12).
To find out how much work they do together in one day, we divide this by 3.
So, the work done by A, B, and C in one day is (1/90 + 1/40 + 1/12) / 3 = 1/60.
This means that they can complete the work in 60 days working together in this way.
Now, let's find out how much work each person does in these 60 days:
- A works for 20 days (since A works every third day), so A does 20 * (1/90) = 2/9 of the work.
- B works for 20 days, so B does 20 * (1/40) = 1/2 of the work.
- C works for 20 days, so C does 20 * (1/12) = 5/3 of the work.
The total amount of money is divided in proportion to the work done, so:
- A gets (2/9) / ((2/9) + (1/2) + (5/3)) * 240 = Rs. 24
- B gets (1/2) / ((2/9) + (1/2) + (5/3)) * 240 = Rs. 54
- C gets (5/3) / ((2/9) + (1/2) + (5/3)) * 240 = Rs. 162
So, the correct answer is: A Rs. 24, B Rs. 54 and C Rs. 162.
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