If 4 (A's capital) = 6 (B's capital) = 10 (C's capital), then out of a profit of ₹ 4650, C will receive

### Concept & Equated Multiples When investments are given as equated multiples (e.g., $xA = yB = zC$), find the ratio of their investments by dividing the entire equation by the Least Common Multiple (LCM) of the coefficients $x, y, \text{ and } z$. ### Step-by-Step Solution * **Given Equality:** * $4A = 6B = 10C$ * **Finding the Ratio:** * Find the LCM of the coefficients 4, 6, and 10. * $\text{LCM}(4, 6, 10) = 60$. * Divide the entire equation by 60: $$ \frac{4A}{60} = \frac{6B}{60} = \frac{10C}{60} $$ $$ \frac{A}{15} = \frac{B}{10} = \frac{C}{6} $$ * This gives the direct investment (and thus profit) ratio: $A : B : C = 15 : 10 : 6$ * **Distributing the Profit:** * Total ratio parts = $15 + 10 + 6 = 31$ parts. * Total profit = ₹ 4650. * Value of 1 part = $\frac{4650}{31} = \text{₹ } 150$. * C's share corresponds to 6 parts. * C's share = $6 \times 150 = \text{₹ } 900$. ### Exam Strategy & Shortcut Instead of LCM, you can use the "cover-up" method. To find A's ratio part, cover 4 and multiply the others ($6 \times 10 = 60$). For B, cover 6 ($4 \times 10 = 40$). For C, cover 10 ($4 \times 6 = 24$). The ratio is $60 : 40 : 24$. Divide by 4 to simplify to $15 : 10 : 6$. ### Common Pitfall Assuming the ratio is directly $4 : 6 : 10$. If $4A = 10C$, A must be larger than C for the equality to hold, meaning the ratio is inverted relative to the coefficients. ### Final Answer Therefore, the correct answer is **₹ 900**.