Question

A man buys goods at $25$% off the list price. He desires to mark the goods so that he can give a discount of $20$% on the marked price and still clear a profit of $25$% on the selling price. What percent of the list price must he mark the goods?

• A. $125$%
• B. $100$%
• C. $80$%
• D. $75$%

Answer 1

Answer: (A)

$125$%

Let's assume list price be $X$ Rs

Cost price (CP) = 25% off list price $=X-\frac{X}{4}=\frac{3X}{4}$

Profit = 25% on the selling price

We know that $SP=CP+Profit$

$\Rightarrow SP=CP+25\%ofSP$

$\Rightarrow SP=\frac{3X}{4}+\frac{25}{100}\times SP$

$\Rightarrow SP-\frac{SP}{4}=\frac{3X}{4}$

$\Rightarrow \frac{3\times SP}{4}=\frac{3X}{4}$

$\therefore SP=X$

Discount = 20%, Let Marked price (MP) be Y.

$\therefore SP=MP-Discount$

$\Rightarrow SP=MP-20\%ofMP$

$\Rightarrow X=Y-\frac{20\times Y}{100}=\frac{4Y}{5}$

$\Rightarrow Y=\frac{5X}{4}$

So, Marked Price $=Y=\frac{5X}{4}$

Hence Marked percentage of the list price $\frac{Markedprice\times 100}{Listedprice}=\frac{\frac{5X}{4}\times 100}{X}=125\%$