Question

A building construction work can be completed by two masons A and B together in 22.5 days. Mason A alone can complete the construction work in 24 days less than mason B alone. Then mason A alone will complete the construction work in :

• A. 42 days
• B. 24 days
• C. 36 days
• D. 30 days

Hint:

For these quadratic equations, you can quickly check options. If \( x=36 \), then \( y=60 \). \( 1/36 + 1/60 = (5+3)/180 = 8/180 = 2/45 \), which matches.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This is a work-time problem. If A takes \( x \) days and B takes \( y \) days, then in one day they complete \( 1/x \) and \( 1/y \) of the work respectively. Together they complete \( 1/22.5 \).
Step 2: Key Formula or Approach:
1. \( \frac{1}{x} + \frac{1}{y} = \frac{1}{22.5} = \frac{2}{45} \).
2. Given \( y = x + 24 \).
Step 3: Detailed Explanation:
Substitute \( y \) in the work equation: \[ \frac{1}{x} + \frac{1}{x+24} = \frac{2}{45} \] \[ \frac{x + 24 + x}{x(x+24)} = \frac{2}{45} \implies \frac{2x + 24}{x^2 + 24x} = \frac{2}{45} \] \[ 45(x + 12) = x^2 + 24x \implies 45x + 540 = x^2 + 24x \] \[ x^2 - 21x - 540 = 0 \] Factorizing: \[ x^2 - 36x + 15x - 540 = 0 \implies x(x-36) + 15(x-36) = 0 \] So, \( x = 36 \) (as days cannot be negative).
Step 4: Final Answer:
Mason A completes the work in 36 days.