A dealer buys a power tiller for ext{Rs. }$1,20,000$. By what percentage above the cost price should the dealer mark the price so that after allowing a cash discount of $15\%$, a net profit of $19\%$ is still realized?
Options:
(A) $40\%$
(B) $34\%$
(C) $42\%$
(D) $38\%$
Answer Key:
A
Step-by-Step Solution & Explanation
**Method 1: Marked Price Factor Formulation**
Let cost price be $\text{CP}$ and marked price factor be $(1 + m)$ so that $\text{MP} = \text{CP}(1 + m)$.
Selling price after $15\%$ discount:
$\text{SP} = \text{MP} \times (1 - 0.15) = 0.85 \times \text{CP}(1 + m)$
To achieve a $19\%$ profit, $\text{SP} = 1.19 \times \text{CP}$:
$0.85(1 + m) = 1.19 \implies 1 + m = \frac{1.19}{0.85} = \frac{119}{85} = \frac{17 \times 7}{17 \times 5} = \frac{7}{5} = 1.40$
$m = 0.40 = 40\%$
Option **A** is correct.