Work and Time: Efficient Methods

Basic Concept

• Work = Rate × Time
• If A completes work in n days, A's one day work = 1/n

Combined Work

• If A does work in a days and B in b days:
• Combined rate = 1/a + 1/b
• Time together = ab/(a+b)

Work and Wages

• Wages ratio = Work ratio = Efficiency ratio
• If A and B work for different times: Wages ratio = (Efficiency × Time) ratio

Pipes and Cisterns

• Inlet pipe: Positive work
• Outlet pipe: Negative work
• Net rate = Sum of all rates

Men-Days Formula

• M₁D₁W₂ = M₂D₂W₁
• (Men × Days × Hours/day) / Work = Constant

CAT Strategy

• Use LCM of days as total work for easier calculations
• Convert all rates to same time unit
• For complex problems, use efficiency ratios