Question

A and B together can do a piece of work in 15 days where as b and c together can do it in 12 days C and A can do it in 20 days how long will they take to finish the work , working together also find the number of days taken by each to do the same work ,working alone

Answer 1

In 1 day, A and B together can do 1/15 workIn 1 day, B and C together can do  1/12 workIn 1 day, C and A together can do  1/20 workIn 1 day, 2*(A,B,C) can do  : 1/15 + 1/12 + 1/20 = 4+5+3/60 = 1/5 work(A,B,C) can do 1 work in 1/10 workSo, (A,B,C) together complete 1 work in 10 days.To find alone working times:A alone, in 1 day: 1/10 - 1/12 = 6-5/60 = 1/60 workA alone can complete a work in 60 days....Similarly B alone complete a work in : 1/ [ 1/10 - 1/20] = 1/ [3/60] = 20days..C alone can complete the same work in: 1/ [1/10 - 1/15] = 1/[2/60] = 30 days.(A+B+C) together do the work in 10 daysA alone in 60 days, B alone in 20 days, C alone in 30 days...[concept: capacity(or)people * days = work, hence work and days are inversly related)

Answer 2

Assuming everybody works at constant rate and independent from each other.

When A works for 5 days and B works for 7 days, we can conclude that A and B work together for 5 days and B works alone for 2 days. And

Work Rate(A+B) = 1/12 (work/day)

Thus, Work is done by A and B for 5 days together = 5 days x 1/12 (work/day) = 5/12 work

When B works for 7-5 = 2 days and C works for 13 day, we can conclude that B and C work together for 2 days and C work alone for 13 - 2 = 11 days.

Work Rate(B+C) = 1/16 (work/day)

Thus, Work is done by B and C for 2 days = 2 days x 1/16 (work/day) = 1/8 work

The remaining job = 1 - 5/12 - 1/8 = (24 - 10 - 3)/24 = 11/24 work

C can finish this part of work within 11 days. Therefore, the work rate for C = 11/24 (work) x 1/11(1/day) = 1/24 (work/day)

Or C can finish one work in = 24 days

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