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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