A grain merchant marks up the cost price of basmati rice by $40\%$. He allows a trade discount of $15\%$ on the marked price and a further cash discount of $5\%$ on the discounted price. The net profit earned by the merchant is ________ % (round off to 2 decimal places).
Answer Key:
13.05
Step-by-Step Solution & Explanation
1. Let Cost Price ($CP$) be $100$.
2. Marked Price ($MP$) after $40\%$ markup:
$MP = 100 \times 1.40 = 140$
3. Price after first discount of $15\%$:
$P_1 = 140 \times (1 - 0.15) = 140 \times 0.85 = 119$
4. Selling Price ($SP$) after second discount of $5\%$:
$SP = 119 \times (1 - 0.05) = 119 \times 0.95 = 113.05$
5. Net Profit Percentage:
$\text{Profit}\% = \frac{113.05 - 100}{100} \times 100\% = 13.05\%$