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A man sold an article for ₹533 by first giving a d% discount on its marked price, and then another discount having the same nominal value (in ₹). If the marked price of the article is ₹1025, then what is the value of d?
22
24
29
21
24
Calculate the total discount amount: 1025 - 533 = 492. Since there are two identical discounts, each is 492 / 2 = 246. Now find what percent 246 is of 1025: (246 / 1025) * 100 = 24%.
Marked Price (MP) = ₹1025, Final Selling Price (SP) = ₹533, Discount value = d% of MP, followed by a second discount of the same monetary value.
SP=MP×(1−100d)−[MP×100d]
Calculate the total discount amount: 1025 - 533 = 492. Since there are two identical discounts, each is 492 / 2 = 246. Now find what percent 246 is of 1025: (246 / 1025) * 100 = 24%.
Many students try to calculate the discounts consecutively (applying the percentage twice), which is incorrect because the problem states the 'nominal value' (amount in ₹) is the same, not the percentage.
Calculate Total Discount
The total discount given is the difference between the Marked Price and the final Selling Price.
Total Discount=1025−533=492
Determine Single Discount Value
Since two discounts of the same nominal value were given, we divide the total discount by 2.
Single Discount=2492=246
Solve for d
The first discount is d% of the Marked Price, which is equal to 246. We set up the percentage equation.
100d×1025=246⟹d=102524600=24
B is correct because the total discount of ₹492 is split into two equal parts of ₹246, and 246 is 24% of 1025.
This concept of 'nominal value' vs 'percentage value' is frequently tested in simple interest problems where fixed amounts are deducted or added.
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