A sum of ₹ 2236 is divided among A, B and C in such a way that A receives $25\%$ more than C and C receives $25\%$ less than B. What is A's share in the amount?

### Concept & Strategy When a total sum is distributed based on relative percentages, the most efficient method is converting the percentage relationships into a combined continuous ratio ($A : B : C$). Using fractions instead of decimals keeps the ratio integers clean and prevents rounding errors. ### Step-by-Step Solution * **Given:** Total Sum = ₹ $2236$. $A = C + 25\%$ of $C = 1.25 \times C = \frac{5}{4} C$. $C = B - 25\%$ of $B = 0.75 \times B = \frac{3}{4} B$. * **Calculation / Deduction:** First, establish the ratios: From $A = \frac{5}{4} C$, we get the ratio $A : C = 5 : 4$. From $C = \frac{3}{4} B$, we get the ratio $C : B = 3 : 4$. To combine them into $A : C : B$, make the common term ($C$) equal. Multiply $A : C$ by $3 \Rightarrow 15 : 12$. Multiply $C : B$ by $4 \Rightarrow 12 : 16$. Combined ratio $A : C : B = 15 : 12 : 16$. So, $A : B : C = 15 : 16 : 12$. Now, calculate the share values. Let the shares be $15x$, $16x$, and $12x$. Total units = $15 + 16 + 12 = 43$ units. $$43 \text{ units} = 2236$$ $$1 \text{ unit} = \frac{2236}{43} = 52$$ We need to find A's share: A's share = $15 \text{ units} = 15 \times 52 = 780$. ### Exam Strategy & Shortcut Use the Ratio Merging Method rapidly. $A:C = 5:4$ and $C:B = 3:4$. Write it like a block: $A \quad C \quad B$ $5 \quad 4$ $\quad \quad 3 \quad 4$ Fill the empty spaces with the adjacent numbers: $5 \quad 4 \quad 4$ $3 \quad 3 \quad 4$ Multiply vertically: $(5 \times 3) : (4 \times 3) : (4 \times 4) = 15 : 12 : 16$. This grid method is much faster than algebraically balancing fractions under time pressure. ### Common Pitfall A common trap is assuming that because A is $25\%$ *more* than C, and C is $25\%$ *less* than B, that A and B are equal. Percentages are relative to their base. A $25\%$ increase on a smaller base ($C$) does not equal a $25\%$ decrease from a larger base ($B$). The ratio method completely bypasses this logical trap. ### Final Answer **Therefore, the correct answer is ₹ 780.**