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 \( W \), and the work rates of A, B, and C be \( A \), \( B \), and \( C \) respectively. Given: \[ \frac{W}{72} = A + B, \quad \frac{W}{120} = B + C, \quad \frac{W}{90} = A + C \] Find the time for A alone. Add the equations: \[ \frac{W}{72} + \frac{W}{120} + \frac{W}{90} = (A + B) + (B + C) + (A + C) \] Simplify: \[ \frac{W}{72} + \frac{W}{120} + \frac{W}{90} = 2A + 2B + 2C \] Further simplification leads to \( A = 60 \) days. Therefore, A alone takes 60 days.