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Question

A shopkeeper sells a saree at 8% profit and a sweater at a 10% discount, thereby, getting a sum of 1008. If she had sold the saree at 10% profit and the sweater at 8% discount, she would have got 1028. Find the cost price of the saree?


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Solution

Let the Cost Price of the saree be x

Let the Cost Price of the Sweater be y

According to the first condition given in the question:

A shopkeeper sells a saree at '8%' profit and a sweater at a 10% discount.

The formula for Selling Price(SP), in terms of Cost Price(CP) and Profit%, SP=100+Profit%100×CP

The selling price (SP) of the saree=100+8100x=108x100………(1)

The Selling Price(SP) of the sweater=y-10y100=90y100……….(2)

Now by adding both the equations [1] and [2], we get.

108x100+90y100=1008

108x+90y=100800……………………………………………(3)

According to the second condition given in the question:

A shopkeeper sells a saree at 10% profit and a sweater at an 8% discount,

The selling price (SP) of the saree=100+10100x=110x100……………….(4)

The selling price (SP) of the sweater=y-8y100=92y100…………………(5)

Now by adding both the equations –[4] and [5], we get,

110x100+92y100=1028

110x+92y=102800…………………………………………….(6)

Now by subtracting equation [3] from equation [6], we get,

2x+2y=2000

x+y=1000

y=1000-x………………………………………………….(7)

Now by substituting the value of y from equation (7) in equation (3), we get,

108x+901000-x=100800108x-90x=100800-9000018x=10800x=600

Therefore, the cost price of a saree is 600


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