A sum of money is shared in the ratio of 3 : 4 : 5. The smallest share is divided again in the ratio of 1 : 2. What fraction of the total sum of money is the larger of the two latter shares?

### Concept & Compounding Ratios When a fractional part of a whole is further subdivided into a new ratio, multiply the respective fractions to find the final proportion relative to the original whole. ### Step-by-Step Solution * Let the total sum of money be divided into $3 + 4 + 5 = 12$ units. * The smallest share corresponds to 3 units, which is $\frac{3}{12} = \frac{1}{4}$ of the total sum. * This smallest share is now subdivided in the ratio of $1 : 2$. * Total parts of this subdivision = $1 + 2 = 3$. * We need to find the "larger of the two latter shares", which corresponds to 2 parts out of 3. * This larger subdivided share is $\frac{2}{3}$ of the smallest original share. * To find its fraction of the total sum, multiply the fractions: $$\text{Fraction} = \frac{2}{3} \times \frac{1}{4}$$ * $\text{Fraction} = \frac{2}{12} = \frac{1}{6}$ ### Exam Strategy & Shortcut Assume a convenient total sum that is highly divisible, like ₹ 120 (since $3+4+5=12$). The shares are 30, 40, and 50. The smallest is 30. Divide 30 in the ratio $1 : 2$, giving parts of 10 and 20. The larger part is 20. The fraction of the total is $\frac{20}{120} = \frac{1}{6}$. ### Common Pitfall Finding the fraction of the smallest share ($\frac{2}{3}$) but forgetting to multiply it by the initial ratio fraction ($\frac{1}{4}$) to find the proportion relative to the *total* sum. ### Final Answer Therefore, the correct answer is **$\frac{1}{6}$**.