An agent sells goods of value of ₹ 15000. The commission which he receives at the rate of $12\frac{1}{2}\%$ is

### Concept & Logic This is a direct application of percentages in a real-world commercial context. The key to solving this instantly is converting the mixed fraction percentage into a simple ratio. The equivalent fraction for $12.5\%$ is a standard value that should be memorized. $$12\frac{1}{2}\% = 12.5\% = \frac{1}{8}$$ ### Step-by-Step Solution **Given:** * Total Sales Value = $₹ 15000$ * Commission Rate = $12\frac{1}{2}\%$ **Calculation / Deduction:** * Identify the fractional equivalent of the given commission rate to bypass decimal division: $12\frac{1}{2}\% = \frac{12.5}{100} = \frac{1}{8}$ * Set up the equation to find the total commission amount: $$\text{Commission} = \frac{1}{8} \times 15000$$ * Perform the division. You can divide by $2$ three times to divide by $8$: First division by 2: $15000 \div 2 = 7500$ Second division by 2: $7500 \div 2 = 3750$ Third division by 2: $3750 \div 2 = 1875$ * The resulting value is the commission earned by the agent. ### Exam Strategy & Shortcut Never use $12.5 \div 100$ when calculating manually. Always use the fraction $\frac{1}{8}$. If you cannot divide $15000$ by $8$ quickly in your head, break it down: $15000$ is $8000 + 7000$. $\frac{1}{8}$ of $8000$ is $1000$. $\frac{1}{8}$ of $7000$ is $875$. Adding them together gives $1875$. ### Common Pitfall A common error is converting $12\frac{1}{2}\%$ to $12.05\%$ or making arithmetic mistakes when multiplying $15000$ by $12.5$ and then dividing by $100$. Relying on the fractional equivalent entirely eliminates decimal errors. ### Final Answer Therefore, the correct answer is **₹ 1875**.