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A 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. 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.182A Rs.22, B Rs.50 and C Rs. 132

Question

A 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. 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.182A Rs.22, B Rs.50 and C Rs. 132

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Solution

To solve this problem, we first need to find out how much work each person does in a day.

  1. A can complete the work in 90 days, so in one day, A does 1/90 of the work.
  2. B can complete the work in 40 days, so in one day, B does 1/40 of the work.
  3. C can complete the work in 12 days, so in one day, C does 1/12 of the work.

Now, let's find out how much work each person does in 3 days (since they work in turns every 3 days):

  1. In 3 days, A does 3*(1/90) = 1/30 of the work.
  2. In 3 days, B does 3*(1/40) = 3/40 of the work.
  3. In 3 days, C does 3*(1/12) = 1/4 of the work.

Adding these up, we find that in 3 days, they complete 1/30 + 3/40 + 1/4 = 1/3 of the work.

So, in 9 days (3 cycles of 3 days), they complete the entire work.

Now, let's find out how much work each person did in these 9 days:

  1. A did 3*(1/30) = 1/10 of the work.
  2. B did 3*(3/40) = 9/40 of the work.
  3. C did 3*(1/4) = 3/4 of the work.

The total amount they get is Rs. 240. So, the amount each person gets is proportional to the work they did:

  1. A gets (1/10)*240 = Rs. 24.
  2. B gets (9/40)*240 = Rs. 54.
  3. C gets (3/4)*240 = Rs. 162.

So, the correct option is A Rs. 24, B Rs.54 and C Rs. 162.

This problem has been solved

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