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?

• A. $600$
• B. $650$
• C. $680$
• D. $690$

Answer 1

The correct option is A $600$

Let Cost Price of saree Rs $x$
Let Cost Price of sweater Rs $y$
According to the $1^{st}$ condition of question
Selling Price of saree is Rs. $x+\frac{8x}{100}$
$=\frac{108x}{100}$ ........(1)
Selling Price of sweater is Rs. $y-\frac{10y}{100}$
$=\frac{90x}{100}$ ........(2)
Adding (1) and (2), we get
$\frac{108x}{100}+\frac{90y}{100}=1008$ .........(3)
According to the $2^{nd}$ condition of question.
Selling Price of saree is Rs. $x+\frac{10x}{100}$
$=\frac{110x}{100}$
Selling Price of Sweater is Rs. $y-\frac{8y}{100}$
$=\frac{92x}{100}$
$\Rightarrow \frac{110x}{100}+\frac{92y}{100}=1028$ .....(4)
Solve (3) and (4)
$108x+90y=100800$ .......(5)
$\Rightarrow 110x+92y=102800$ .......(6)
Subtract (6) $-$ (5), we have
$2x+2y=2000$
$\Rightarrow x+y=1000$ (7)
Substitute (7) in (5), we get
$108x+90(1000-x)=100800$
$\Rightarrow 108x-90x=100800-90000$
$\Rightarrow 18x=10800$
$\Rightarrow x=600$
Cost of saree is Rs $600$