A sum of ₹ 731 is divided among A, B and C such that A receives 25% more than B and B receives 25% less than C. What is C's share in the amount? (Bank P.O., 2006)

### Concept & Chained Ratios When shares are linked by percentages, it is easiest to set the final person in the chain to a base value (like 100 or a variable $x$) and work backward to express all shares in terms of that base. $$ \text{Final Share} = \frac{\text{Individual Ratio}}{\text{Sum of Ratios}} \times \text{Total Amount} $$ ### Step-by-Step Solution 1. **Define variables working backward:** Let C's share be $x$. 2. **Express B's share:** B receives 25% less than C. $B = x - 0.25x = 0.75x = \frac{3}{4}x$ 3. **Express A's share:** A receives 25% more than B. $A = B + 0.25B = 1.25B = \frac{5}{4}B$ Substitute B's value: $A = \frac{5}{4} \times \left(\frac{3}{4}x\right) = \frac{15}{16}x$ 4. **Find the combined ratio A : B : C:** $A : B : C = \frac{15}{16}x : \frac{3}{4}x : x$ To clear the denominators, multiply the entire ratio by 16: $A : B : C = 15 : 12 : 16$ 5. **Calculate C's share:** Total ratio parts = $15 + 12 + 16 = 43$. Total amount = ₹ 731. $C = \frac{16}{43} \times 731$ $C = 16 \times 17 = 272$ ### Exam Strategy & Shortcut Instead of fractions, use numbers! Let C = 160 (a number easily divisible by 4 twice). B is 25% less: $160 - 40 = 120$. A is 25% more than B: $120 + 30 = 150$. Ratio is $150 : 120 : 160 = 15 : 12 : 16$. Sum = $43 \implies 43 \text{ units} = 731 \implies 1 \text{ unit} = 17$. C's share = $16 \text{ units} = 16 \times 17 = 272$. ### Common Pitfall A frequent error is calculating "25% more" or "25% less" based on the same base amount. Percentages are strictly relative to their immediate reference points (B is relative to C, A is relative to B). ### Final Answer Therefore, the correct answer is **None of these**.