Question

A shopkeeper allows a discount of 10% on an article and gives one article free for every fifteen articles bought by a customer. If he still gains 35% in this transaction, then the marked price of the article exceeds the cost price by

1. 60%
2. 50%
3. 40%
4. 30%

Answer 1

Correct Answer - Option 1 : 60%

Given:

He sold 16 articles for the price of 15 articles

He gains 35% profit on 16 articles

Discount is 10%

Formula Used:

Selling price = (100 – D)% of Marked price

Calculation:

Let the Marked price be Rs. 100

⇒ Selling price = D% of Marked price

⇒ Selling price = 90/100 × 100

⇒ Selling price = Rs. 90

He sold 15 articles for Rs. 90

⇒ Total Selling price he got = 15 × 90

⇒ Total Selling price he got = Rs. 1,350

He gained 35% on the whole 16 articles,

⇒ Cost price of 16 articles = 1,350/(100 + 35) × 100

⇒ Cost price of 16 articles = 1,350/135 × 100

⇒ Cost price of 16 articles = 1,000

⇒ Cost price of 1 article = 1,000/16

⇒ Cost price of 1 article = 125/2

Difference between Marked price and Cost price of 1 article,

⇒ 100 – 125/2

⇒ 75/2

Percentage difference,

⇒ {(75/2)/125/2} × 100

⇒ 3/5 × 100

⇒ 60%

∴ The difference between Marked and Cost price is 60%.