A company calculates its profit or loss quarterly. The company makes 25% profit, 20% loss and 20% loss in three consecutive quarters. What minimum profit or loss should the company make in fourth quarter to have no loss overall?
20% profit
20% loss
25% profit
25% loss
Answer is Right!
Answer is Wrong!
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UPSC CISF-AC-EXE – 2024
Quarter 1: Profit of 25%. Capital becomes $C \times (1 + 0.25) = 1.25C$.
Quarter 2: Loss of 20%. Capital becomes $1.25C \times (1 – 0.20) = 1.25C \times 0.80 = C$.
Quarter 3: Loss of 20%. Capital becomes $C \times (1 – 0.20) = C \times 0.80 = 0.8C$.
After three quarters, the capital is $0.8C$.
We need $0.8C \times (1+p) \ge C$.
Dividing by $0.8C$ (assuming $C>0$): $1+p \ge \frac{C}{0.8C} = \frac{1}{0.8} = \frac{1}{4/5} = 1.25$.
$p \ge 1.25 – 1 = 0.25$.
So, the minimum profit percentage in the fourth quarter must be $0.25 \times 100\% = 25\%$.