Shortcut Trick Efficiency Ratio A : B : C B is 75% less efficient than A → B = 0.25 × A C is 80% more efficient than B → C = 1.8 × B = 1.8 × 0.25A = 0.45A Total Work = Efficiency of A × 90 = 1 × 90 = 90 units Work by B and C (30 days) = (0.25 + 0.45) × 30 = 0.7 × 30 = 21 units Remaining Work = 90 − 21 = 69 units. Time for A = 69 ÷ 1 = 69 days ∴ The correct answer is 69 days. Alternate Method Given: A's time = 90 days. B's efficiency = 25% of A. C's efficiency = 180% of B. +--------+-------------------------+------------------------+ | Person | Efficiency Calculation | Efficiency (Units/Day) | +--------+-------------------------+------------------------+ | A | Assumed base efficiency | 100 | | B | 100 − 75% | 25 | | C | 25 + 80% of 25 | 45 | +--------+-------------------------+------------------------+ ⇒ Total Work = Efficiency of A × Days = 100 × 90 = 9000 units ⇒ Efficiency of (B + C) = 25 + 45 = 70 units/day ⇒ Work done by B and C in 30 days = 70 × 30 = 2100 units ⇒ Remaining work = 9000 − 2100 = 6900 units ⇒ Time taken by A alone = Remaining Work ÷ Efficiency of A = 6900 ÷ 100 = 69 days ∴ The correct answer is 69 days. Related Concepts: Efficiency and Time Relationship Efficiency is inversely proportional to the time taken to complete a work. If efficiency ratio is x : y, the time ratio is y : x. Total Work Formula Total Work = Efficiency × Time. This is the fundamental equation for all Time and Work problems. Combined Efficiency When multiple people work together, their individual efficiencies are added to find the combined rate of work per day.