A and B can do a piece of work in 12 days B and C in 15 days C and A in 20 days then that numbers of days taken by A B and C together to finish the work are?

Correct answer

10 days

Explanation

Explanation A and B can do the work in 12 days, so their combined rate of work is 1/12 of the work per day. B and C can do the work in 15 days, so their combined rate of work is 1/15 of the work per day. C and A can do the work in 20 days, so their combined rate of work is 1/20 of the work per day. Now, let's add the three equations and simplify: 2(A + B + C) = 1/12 + 1/15 + 1/20 Combine like terms: 2(A + B + C) = (10 + 8 + 6) / 120 Simplify the fraction: 2(A + B + C) = 24 / 120 Divide both sides by 2: A + B + C = 12 / 120 Simplify the fraction: A + B + C = 1/10 So, A, B, and C together can complete 1/10 of the work in one day. To find the number of days taken by A, B, and C together to finish the work, we take the reciprocal: Number of days = 1 / (1/10) = 10 days