Question : A tradesman marks his goods $30\%$ more than the cost price. If he allows a discount of $6\frac{1}{4}\%$, then his gain percent is:
Option 1: $23\frac{3}{4}\%$
Option 2:
$22\%$
Option 3: $21\frac{7}{8}\%$
Option 4:
$30\%$
Correct Answer: $21\frac{7}{8}\%$
Solution :
Using, Marked price = Cost price + Mark-up value
Selling price = Marked price – Discount
Let the cost price as $x$.
The marked price would then be $1.30x$.
The discount of $6\frac{1}{4}\%$ on the marked price $=\frac{25}{400}\times1.30x = 0.08125x$
The selling price after the discount $=1.30x - 0.08125x = 1.21875x$
The gain percent $=\frac{(1.21875x - x)}{x}\times100 =21.875\%= 21\frac{7}{8}\%$
Hence, the correct answer is $21\frac{7}{8}\%$.
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