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.

Answer 1

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.