A dealer allowed a discount of 25% on the marked price of Rs 12000 on an article and incurred a loss of 10%. What discount should he allow on the marked price so that he gains Rs 440 on the article?a)11%b)13%c)19%d)15%e)None of theseCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Given:
Marked price (MP) = Rs 12000
Discount = 25%
Loss = 10%

To find:
Discount to be allowed to gain Rs 440 on the article

Solution:

Let's first calculate the selling price (SP) of the article after allowing a discount of 25% on the marked price.

Discount = 25%
Discount amount = 25% of MP = 0.25 * 12000 = Rs 3000
Selling price = MP - Discount amount = 12000 - 3000 = Rs 9000

Now, we know that the dealer incurs a loss of 10% on the selling price of Rs 9000. This means that the cost price (CP) of the article is more than Rs 9000.

Loss = 10%
Loss amount = 10% of SP = 0.1 * 9000 = Rs 900
CP = SP + Loss amount = 9000 + 900 = Rs 9900

To gain a profit of Rs 440 on the article, the dealer needs to sell it at a selling price of CP + Profit = 9900 + 440 = Rs 10340

Let's calculate the discount that the dealer should allow on the marked price to sell the article at Rs 10340.

Discount amount = MP * (Discount % / 100) = MP * (x / 100)
SP = MP - Discount amount
SP = 10340
MP - MP * (x / 100) = 10340
MP * (1 - x / 100) = 10340
MP = 10340 / (1 - x / 100)

Substituting MP = Rs 12000, we get:

12000 = 10340 / (1 - x / 100)
1 - x / 100 = 10340 / 12000
x / 100 = 1 - 1034 / 1200
x = 13.83

Therefore, the dealer should allow a discount of 13.83% on the marked price to gain a profit of Rs 440 on the article.

Hence, the correct option is (b) 13%.

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