A and B can do a piece of work in 72 days. B and C can do it in 120 days. A and C can do it in 90 days. In what time can A alone do it? 

A and B can do a piece of work in 72 days. B and C can do it in 120 days. A and C can do it in 90 days. In what time can A alone do it?

A alone can work in 120 days.

Given :

A + B = 1/ 72

B + C = 1/ 120

A + C = 1 / 90

Now, We have to find the work done by A alone.

A + B + B + C + A + C = 1/72 + 1/120 + 1/90

2 ( A + B + C) = 1/72 + 1/120 + 1/90 ===> Eqn 1

Solving the above equation

2 ( A + B + C) = ( 5 + 3 + 4) / (360)

2 ( A + B + C) = 12 / 360 ==> 1/30

A+ B + C = 1/30 x 1/2

A+ B + C = 1/ 60

Now, Subtract B and C 's work from A

A = 1/60 - B + C

A = 1/60 - 1/120 ===> 1/120

So, A alone can work in 1/120 days.

Example Sums to Work out

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