# A man marks his articles at 35% more than the cost price. He sells 50% articles on marked price, 30% articles at 10% discount on marked price and remaining articles at 20% discount on marked price. What is his overall profit percentage?

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UPPCL Assistant Accountant 29 Jan 2019 Official Paper
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1. 26.75%
2. 28.25%
3. 25.55%
4. 22.75%

Option 3 : 25.55%

## Detailed Solution

Given:

The marked price = 135% of cost price

Formula used:

$$GM \% = {GM \over TM} × 100$$

(Where, GM = Gain marks, TM = Total marks)

$$P \% = {SP - CP \over CP} × 100$$

(Where P = Profit, SP = Selling price, CP = Cost price)

Calculation:

Let us assume cost price of the article be X and the total number of items is 100

⇒ The total expenditure of the man = 100X

⇒ Marked price = 135% of X

⇒ Sales of 50% of the article = (100/2) × (135X/100) = 67.5X

⇒ Sales of 30% of the article = 100 × (30/100) × (135X/100) × (90/100) = 36.45X

⇒ Sales of remaining 20% of the article = 100 × (20/100) × (135X/100) × (80/100) = 21.6X

⇒ Total sales of the articles = 67.5X + 36.45X + 21.6X = 125.55X

⇒ The profit % of the man = $$= {125.55X - 100X \over 100X} \times 100$$

By solving profit % = 25.55%

∴ The required result will be 25.55%.
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