Question

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

• A. 110 days
• B. 120 days
• C. 60 days
• D. 55 days

Hint:

When working with rates of work, add and subtract the equations to eliminate common terms and isolate the desired variable.

Answer 1

The Correct Option is C

Let the work be represented by \( W \), and let the rates of work for A, B, and C be \( A \), \( B \), and \( C \) respectively. From the given information: \[ \frac{W}{72} = A + B, \quad \frac{W}{120} = B + C, \quad \frac{W}{90} = A + C \] We want to find the time taken by A alone. First, add all three equations: \[ \frac{W}{72} + \frac{W}{120} + \frac{W}{90} = (A + B) + (B + C) + (A + C) \] Simplifying: \[ \frac{W}{72} + \frac{W}{120} + \frac{W}{90} = 2A + 2B + 2C \] Now simplify further to find \( A \) and calculate the time. This simplifies to \( A = 60 \) days. Thus, A alone can do the work in 60 days.