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Q $1$ . A shopkeeper marks shirts at $25\%$ above cost price then allows a discount of $10\%$ . What is the profit or loss $\%$ ?

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Find the percent: tax, discount, and more

Full solution

Q. Q

1

. A shopkeeper marks shirts at

25\%

above cost price then allows a discount of

10\%

. What is the profit or loss

\%

?

Calculate Marked-up Price: Calculate the marked-up price. $\newline$ Cost price = $\$100$ (assuming for simplicity) $\newline$ Mark-up = $25\%$ of cost price $\newline$ Marked-up price = Cost price + ( $25\%$ of Cost price) $\newline$ = $\$100$ + ( $\$100 \times 0.25$ ) $\newline$ = $\$100$ + $\$25$ $\newline$ = $\$125$
Calculate Selling Price: Calculate the selling price after discount. $\newline$ Discount = $10\%$ of marked-up price $\newline$ Selling price = Marked-up price - ( $10\%$ of Marked-up price) $\newline$ = $\$125 - (\$125 \times 0.10)$ $\newline$ = $\$125 - \$12.5$ $\newline$ = $\$112.5$
Calculate Profit Percentage: Calculate the profit or loss percentage. $\newline$ Profit or Loss = Selling price - Cost price $\newline$ = $\$112.5$ - $\$100$ $\newline$ = $\$12.5$ $\newline$ Profit or Loss percentage = $\frac{\text{Profit or Loss}}{\text{Cost price}} \times 100$ $\newline$ = $\frac{\$12.5}{\$100} \times 100$ $\newline$ = $12.5\%$

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