If a merchant offers a discount of 25\% on the list price, then he makes a loss of 5\% . What \% profit or \%

Question

If a merchant offers a discount of 25\% on the list price, then he makes a loss of 5\% . What \% profit or \% loss will he make if he sells at a discount of 10\% of the list price?

Accepted Answer

Let the list price (Marked Price, MP) be

100

.Case 1: Discount =

25%

$

Selling Price (SP)_{1} = 100 - 25 = 75

L oss =

5\%

, w hi c hm e an s

\text{SP}_1 = 95\%

o f C os tP r i ce (CP) :

0.95 \times CP = 75 ⟹ CP = \frac{75}{0.95} = \frac{7500}{95} = \frac{1500}{19}

C a se 2 : D i sco u n t =

10\%

$\text{Selling Price (SP)}_2 = 100 - 10 = 90

Now, profit/loss percentage:

Profit = SP_{2} - CP = 90 - \frac{1500}{19} = \frac{1710 - 1500}{19} = \frac{210}{19}

Profit % = (\frac{Profit}{CP}) \times 100 = (\frac{210/19}{1500/19}) \times 100 = \frac{210}{1500} \times 100 = \frac{210}{15} = 14%

Since the result is positive, it is a

14%

profit.

If a merchant offers a discount of $25%$ on the list price, then he makes a loss of $5%$ . What $%$ profit or $%$ loss will he make if he sells at a discount of $10%$ of the list price?

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If a merchant offers a discount of 25% on the list price, then he makes a loss of 5%. What % profit or % loss will he make if he sells at a discount of 10% of the list price?