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  • A shopkeeper sells a saree at 8% profit and a sweater at 10% discount, there by, 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

A shopkeeper sells a saree at 8% profit and a sweater at 10% discount, there by, 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.

 

Answers (1)

Solution:
Let the cost price of saree = Rs. x
Let the cost price of sweater = Rs. y
Saree with 8% profit =  (1+\frac{8}{100})x=\frac{108x}{100}
Sweater with 10% discount = (1-\frac{10}{100})y = \frac{90y}{100}
Saree with 10% profit = x + x\times \frac{10}{100}= \frac{110x}{100}

Sweater with 8% discount = y –  y\times \frac{8}{100}= \frac{92y}{100}

According to question:

\frac{108x}{100}+ \frac{92y}{100}= 1008
108x + 90y = 100800         
6x + 5y = 5600 … (1)             (Divide by 18)

\frac{110x}{100}+ \frac{92y}{100}= 1028
110x + 92y = 102800
55x + 56y = 51400 … (2)          (Divide by 2)
Multiply equation (1) by 46 and eq. (2) by  5
276 x + 230 y = 257600
275 x + 230 y = 257000
–              –             –
x = 600
Put x = 600 in eq. (1)
6(600) + 5y = 5600
5y = 5600 –3600
5y = 2000
y = 400
Price of saree = Rs. 600
Price of sweater = Rs. 400
 

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