Question

A and B can do a piece of work in 18 days, B and C can do it in 24 days while C and A can finish it in 36 days. In how many days can A,B and C finish it, if they all work together? In how many days will each one of them finish it working alone​

Answer 1

$\boxed {\boxed{ { \green{ \bold{ \underline{Verified \: Answer \: }}}}}}$

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A and B can do a piece of work in 18 days, B and C can do it in 24 days while C and A can finish it in 36 days. In how many days can A,B and C finish it, if they all work together? In how many days will each one of them finish it working alone

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$\bigstar{\underline{\underline{{\sf\ \red{ SOLUTION:-}}}}}$

Let Total Work = LCM(18,24,36) = 72 units

A + B = 4 units per day

B + C = 3 units per day

A + C = 2 units per day

Add all three equations :

2(A + B + C) = 9

=> A + B + C = 9/2

=> C = 9/2 - (A + B) = 9/2 - 4 = 1/2

=> C alone can complete the work alone in 72/(1/2) = 144 days.

A alone = 9/2 - 3 = 3/2 per day or 72/(3/2) = 48 days.

B alone = 9/2 - 2 = 5/2 per day or 72/(5/2) = 28.8 days.

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