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Trader A gives a single discount of 25% and Trader B gives two successive discounts of 20% and 5% on an identical item. If the discount given by A is Rs. 320 more than the discount given by B, then what is the marked price (in Rs.) of the item? 

Trader A gives a single discount of 25% and Trader B gives two successive discounts of 20% and 5% on an identical item. If the discount given by A is Rs. 320 more than the discount given by B, then what is the marked price (in Rs.) of the item?  Correct Answer 32000

Given:

Trader A gives a single discount of 25%.

Trader B gives two successive discounts of 20% & 5%.

The discount given by A is Rs. 320 more than the discount given by B.

Concept used:

Selling price = Marked price - Discount

Selling price = Marked price × (1 - Discount percentage/100) 

Calculation:

Let the marked price of the product be Rs. 1000P.

So,

The selling price of Trader A = 1000P - (1000P × 1/4) = 750P

Now,

The price of Trader B after first discount = 1000P - (1000P × 1/5) = 800P

The final selling price of Trader B after the final discount = 800P - (800P × 1/20) = 760P

According to the question,

760P - 750P = 320

⇒ 10P = 320

⇒ P = 32

⇒ 1000P = 32000

∴ The original marked price of the article is Rs. 32000. 

Shortcut Trick  Trader A gave 25% discount

Trader B gave two successive discount of 20% & 5% which is equal to (20 + 5 - 100/100) = 24%

According to the questions,

This difference of (25 - 24)% = 1% means Rs. 320.

So, 100% means Rs. 32000

∴ The original marked price of the article is Rs. 32000. 

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