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A man sold an article for ₹360 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 ₹2250, then what is the value of d?
41
38
42
45
42
Since two discounts of d% of MP are applied, total discount value is 2 * (d/100 * 2250). Subtract this from 2250 to equate to 360, then solve for d linearly.
Marked Price (MP) = ₹2250, Final Selling Price (SP) = ₹360, Two consecutive discounts of value 'd% of MP'.
SP=MP×(1−100d)−MP×100d
Since two discounts of d% of MP are applied, total discount value is 2 * (d/100 * 2250). Subtract this from 2250 to equate to 360, then solve for d linearly.
Students often incorrectly use the compound discount formula (1−d/100)2, but the question specifies 'nominal value' (the absolute amount) is identical for both discounts.
Define discount amount
Let the discount percentage be d. Each discount amount in rupees is d% of MP=100d×2250=22.5d.
Discount Value=22.5d
Set up the equation
Since two discounts of the same nominal value are applied, total reduction is 2×22.5d=45d. The Selling Price is MP−45d=360.
2250−45d=360
Solve for d
Subtract 360 from 2250: 1890=45d. Now divide by 45: d=1890/45=42.
d=42
C is correct because the total discount of 1890 represents two equal parts of 945 each, which is 42% of 2250.
This logic is similar to problems involving 'Flat vs Compound' interest, where recognizing the difference between nominal value and multiplicative rates prevents major calculation errors.
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