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A man sold an article for ₹687 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 ₹1145, then what is the value of d?
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Calculate total discount: 1145 - 687 = 458. Since the discount is applied twice as the same nominal value, each discount is 458 / 2 = 229. Then 229 is what percentage of 1145? (229 / 1145) * 100 = 20%.
Marked Price MP = ₹1145, Selling Price SP = ₹687. Two successive discounts are given, each having the same nominal value X in ₹.
SP=MP−2X and X=100d×MP
Calculate total discount: 1145 - 687 = 458. Since the discount is applied twice as the same nominal value, each discount is 458 / 2 = 229. Then 229 is what percentage of 1145? (229 / 1145) * 100 = 20%.
Students often apply the formula for successive percentage discounts (d%) twice, which is incorrect because the question specifies the 'nominal value' (the absolute rupee amount) of the discount is the same.
Calculate Total Discount
The total discount given is the difference between the Marked Price and the Selling Price.
Total Discount=1145−687=458
Calculate Individual Discount Value
Since two discounts of the same nominal value are provided, we divide the total discount by 2.
X=2458=229
Calculate Percentage Rate d
Calculate what percentage 229 is of the initial Marked Price 1145.
d=(1145229)×100=20%
C is correct because the individual discount value is ₹229, which is exactly 20% of the ₹1145 marked price.
This concept of 'nominal value' vs 'percentage rate' is critical in banking exams (Interest calculations) where simple interest and compound interest formulas distinguish between fixed amounts and rates.
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