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Question
A shopkeeper gives two successive discounts on an article whose marked price is ₹ 180 and selling price is ₹ 108. Find the first discount percentage if the second discount is 25%
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Solution
Marked price is given as ₹ 180
Let 1st discount be d1 % = ? ...(to find)
2nd discount be d2 % = 25%
Selling price is 108 ...(given)
Price after 1st discount = `180(1 - ("d"_1)/100)` = P ...(1)
Price after 2nd discount = `"P"_1 (1 - ("d"_2)/100)` = 108
Substituting for P1 from (1), we get
`180(1 - ("d"_1)/100)(1 - ("d"_2)/100)` = 108
⇒ Since d2 = 25, we get
`180(1 - ("d"_1)/100)(1 - 25/100)` = 108
∴ `(1 - ("d"_1)/100) = 108/180 xx 100/75 = 4/5`
`1 - ("d"_1)/100 = 4/5`
∴ `("d"_1)/100 = 1 - 4/5 = 1/5`
∴ d1 = `1/5 xx 100` = 20%
1st discount = 20%
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