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After getting two successive discounts, a shirt with a list price of ₹150 is available at ₹105. If the second discount is 12.5%, then find the first discount.
25%
20%
15%
12%
20%
Use the ratio method: 12.5% is 1/8, so the multiplier is 7/8. Divide 105 by (7/8) to get the intermediate price, then compare with 150 to find the first discount.
List price = ₹150, Final selling price = ₹105, Second discount = 12.5%
SP=MP×(1−d1)×(1−d2)
Use the ratio method: 12.5% is 1/8, so the multiplier is 7/8. Divide 105 by (7/8) to get the intermediate price, then compare with 150 to find the first discount.
Students often try to add the percentages or subtract 12.5% from the total discount percentage directly, which is incorrect for successive discounts.
Calculate price after first discount
Let the first discount be x. The second discount of 12.5% means the price becomes 105 after multiplying by (1−0.125)=0.875 or 7/8. Let P1 be the price after the first discount. Thus, P1×87=105.
P1=105×78=120
Calculate the first discount
The list price is 150 and the price after the first discount is 120. The discount amount is 150−120=30.
Discount1=150−120=30
Convert discount amount to percentage
Calculate the percentage based on the original list price of 150.
d1=15030×100=20%
B is correct because the calculated first discount is 20%.
This concept of successive changes is identical to calculating compound interest or population growth rates where values are scaled sequentially.
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