Question : A trader allows a 40% discount on his goods, but he loses 30% on them. Find the percentage of the marked price above the cost price.
Option 1: $15\frac{2}{3}\%$
Option 2: $15 \frac{1}{3} \%$
Option 3: $16 \frac{2}{3} \%$
Option 4: $16 \frac{1}{3} \%$
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Correct Answer: $16 \frac{2}{3} \%$
Solution : Let the marked price (MP) be 100$x$ After a discount of 40%, the selling price = 60$x$ When a loss of 30% then, $\frac{70}{100}$ of cost price (CP) = 60$x$ ⇒ CP = $\frac{600x}{7}$ Difference in MP and CP = 100$x$ – $\frac{600x}{7}$ = $\frac{100x}{7}$ Mark up% = $\frac{\text{Mark up value}}{\text{CP}}$ × 100 = $\frac{\frac{100x}{7}}{\frac{600x}{7}}$ × 100 = $\frac{100}{6}$ = $16\frac{2}{3}\%$ Hence, the correct answer is $16\frac{2}{3}\%$.
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