Question

To finish a work, b will take three times as long as a and c together and c will take twice as long as a and b together. If the three persons a, b and c together can finish the work in 20 days , then how long will a take to finish the work alone?

Answer 1

assume 100 units of work, so together they work @ 10 units/day
let A, B, C work @ a,b,c units /day
(a+c) = 3b ....... (i)
(a+b) = 2c ....... (ii)
a+b+c = 10 ..... (iii)

solving the system , we get
a = 25/6, b = 5/2, c = 10/3
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A will take 100/(25/6) = 24 days
B will take 100/(5/2) = 40 days
C will take 100/(10/3) = 30 days