Question

A and B can do a work in 120 days, B and C can do it in 72 days while A and C can do it in 90 days. In how many days can C alone do the work?

• A. 30
• B. 60
• C. 40
• D. 120

Hint:

Use LCM for total work and set up equations from team combinations. Then isolate individual contributions to find required values.

Answer 1

The Correct Option is D

Let the total work be LCM of 120, 72, and 90 = 360 units. - A + B's 1 day work = \( \frac{360}{120} = 3 \) units - B + C's 1 day work = \( \frac{360}{72} = 5 \) units - A + C's 1 day work = \( \frac{360}{90} = 4 \) units Now, \[ (A + B) + (B + C) + (A + C) = 3 + 5 + 4 = 12 \Rightarrow 2A + 2B + 2C = 12 \Rightarrow A + B + C = 6 \] Subtract A + B = 3: \[ C = 6 - 3 = 3 \text{ units/day} \Rightarrow C alone will take \( \frac{360}{3} = 120 \) days