A sum of ₹ 6400 is divided among three workers in the ratio $\frac{3}{5} : 2 : \frac{5}{3}$. The share (in rupees) of the second worker is (S.S.C., 2007)

### Concept & Simplifying Fractional Ratios To divide a total sum based on a ratio containing fractions, you must first convert the fractional ratio into an equivalent integer ratio by multiplying all terms by the Least Common Multiple (LCM) of the denominators. $$ \text{Equivalent Integer Ratio} = \text{Fractional Ratio} \times \text{LCM}(\text{Denominators}) $$ ### Step-by-Step Solution 1. **Identify the fractional ratio:** The given ratio is $\frac{3}{5} : 2 : \frac{5}{3}$ Note that $2$ can be written as $\frac{2}{1}$. Denominators are 5, 1, and 3. 2. **Find the LCM:** The LCM of 5 and 3 is 15. 3. **Convert to an integer ratio:** Multiply each term in the ratio by 15: First term: $\frac{3}{5} \times 15 = 3 \times 3 = 9$ Second term: $2 \times 15 = 30$ Third term: $\frac{5}{3} \times 15 = 5 \times 5 = 25$ The simplified ratio is $9 : 30 : 25$. 4. **Calculate the share of the second worker:** Total ratio parts = $9 + 30 + 25 = 64$. Total sum = ₹ 6400. Second worker's share = $\frac{30}{64} \times 6400$ Second worker's share = $30 \times 100 = 3000$. ### Exam Strategy & Shortcut Recognize immediately that the sum of the integer ratio parts ($9 + 30 + 25 = 64$) matches the significant digits of the total amount ($6400$). This makes the multiplier exactly $100$. You can instantly see the second worker's share is $30 \times 100 = 3000$ without writing out the full division. ### Common Pitfall Forgetting to multiply the middle integer ($2$) by the LCM. Students often just multiply the fractions by the LCM and leave the integer as $2$, incorrectly creating the ratio $9 : 2 : 25$. ### Final Answer Therefore, the correct answer is **3000**.