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Question
A shopkeeper sells a saree at 8% profit and a sweater at 10% discount, thereby, getting a sum Rs 1008. If she had sold the saree at 10% profit and the sweater at 8% discount, she would have got Rs 1028. Find the cost price of the saree and the list price (price before discount) of the sweater.
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Solution
Let the cost price of the saree and the list price of the sweater be ₹ x and ₹ y, respectively.
Case I: Sells a saree at 8% profit + Sells a sweater at 10% discount = ₹ 1008
⇒ (100 + 8)% of x + (100 – 10)% of y = 1008
⇒ 108% of x + 90% of y = 1008
⇒ 1.08x + 0.9y = 1008 ......(i)
Case II: Sold the saree at 10% profit + Sold the sweater at 8% discount = ₹ 1028
⇒ (100 + 10)% of x + (100 – 8)% of y = 1028
⇒ 110% of x + 92% of y = 1028
⇒ 1.1x + 0.92y = 1028 .....(ii)
On putting the value of y from equation (i) into equation (ii), we get
`1.1 xx 0.92((1008 - 1.08x)/0.9)`
⇒ 1.1 × 0.9x + 927.36 – 0.9936x = 1028 × 0.9
⇒ 0.99x – 0.9936x = 925.2 – 927.36
⇒ –0.0036x = –2.16
∴ x = `2.16/0.0036` = 600
On putting the value of x in equation (i), we get
1.08 × 600 + 0.9y = 1008
⇒ 648 + 0.9y = 1008
⇒ 0.9y = 1008 – 648
⇒ 0.9y = 360
⇒ y = `360/0.9` = 400
Hence, the cost price of the saree and the list price (price before discount) of the sweater are ₹ 600 and ₹ 400, respectively.
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