A shopkeeper marks the price of an article 10% more than the cost price. After allowing discount, he earns 5% profit. The discount percentage is:

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  1. 4.54%
  2. 5.54%
  3. 3%
  4. 4%

Answer (Detailed Solution Below)

Option 1 : 4.54%
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Detailed Solution

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Given:

Marked price = 110% of Cost price

Selling price= 105% of Cost price

Formula used:

Discount % = Discount×100/Marked price 

Calculation:

Let the CP be Rs. 100. 

Then, the MP will be Rs.110

The SP is Rs. 100 + 5% of 100 = 105

Now, Discount percentage

= Discount × 100/MP

= (110 - 105)×100/110

= 500/110

= 50/11

= 4.54%

∴ The Required discount percentage value is 4.54%.

Shortcut Trick

P = MP - D - MP × D/100

Where, P = Profit, D = Discount

⇒ 5 = 10 - D - 10D/100

⇒ -5 = - D - 10D/100

⇒ D = 50/11 = 4.54%

∴ The Required discount percentage value is 4.54%.

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