Question
An item is marked up by Q% above its cost price. If a
shopkeeper gives a 30% discount and still makes a profit of 40%, what discount should be given to achieve a profit of 65%?Solution
Let Cost Price (CP) = ₹100. Marked Price (MP) = ₹(100 + Q). After a 30% discount: Selling Price (SP) = ₹(100 + Q) × 0.70. Given that profit is 40%: SP = ₹100 × 1.40 = ₹140. So, 0.70 × (100 + Q) = 140. 100 + Q = 200 Q = 100. To achieve a 65% profit: Required SP = ₹100 × 1.65 = ₹165. New discount (D) on marked price ₹200: 165 = 200 × (1 - D). 1 - D = 165/200 = 0.825. D = 0.175. The required discount is 17.5%.
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