Question

Trader A gives a single discount of 45% and Trader B gives two successive discounts of 35% and 10% on an identical item of the same marked price. If the discount given by A is ₹539 more than the discount given by Trader B, then what is the marked price (in ₹) of the item?

• A. 15,600
• B. 16,500
• C. 14,500
• D. 15,400

Answer 1

Answer:

D. 15,400

Let marked price = ₹(x)

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Trader A:

Single discount = 45%
$\text{Discount}_A = 0.45x$

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Trader B:

Successive discounts 35% and 10%

Equivalent discount:
= 1 - (1 - 0.35)(1 - 0.10)
$= 1 - (0.65 \times 0.90)$
= 1 - 0.585 = 0.415 = 41.5%
$\text{Discount}_B = 0.415x$

Given:

0.45x - 0.415x = 539

0.035x = 539

Solve:

$x = \frac{539}{0.035} = 15400$

Final Answer: ₹15,400