Name: Linear Equations With One or More Variables
Uploaded: 2019-07-19
Duration: 11 min 20 s
Description: Let's learn the concept of linear equations, the introduction of linear algebra, the formation of linear equations in one, two and three variables, etc.

Question

A shopkeeper sells a saree at

8 %

profit and a sweater at

10 %

discount, thereby getting a sum of

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 that of the sweater.

Accepted Answer

Let the cost price of a saree $= Rs . x$

Let the cost Price of sweater $= Rs . y$

Case I : (S.P. of a saree at $8 %$ profit) $+$ (S.P. of a sweater at $10 %$ discount) $= Rs . 1008$

$\Rightarrow (x + \frac{8 x}{100}) + (y - \frac{10 y}{100}) = 1008$

$\Rightarrow \frac{108 x}{100} + \frac{90 y}{100} = 1008$

$\Rightarrow 108 x + 90 y = 100800$

$\Rightarrow 6 x + 5 y = 5600$ ............(i)

Case II : (S.P. of a saree at $10 %$ profit) $+$ (S.P. of a sweater at $8 %$ discount) $= Rs . 1028$

$\Rightarrow (x + \frac{10 x}{100}) + (y - \frac{8 y}{100}) = 1028$

$\Rightarrow \frac{110 x}{100} + \frac{92 y}{100} = 1028$

$\Rightarrow 110 x + 92 y = 102800$

$\Rightarrow 55 x + 46 y = 51400$ .............(ii)

Multiplying equation (i) by $46$ , we get

$275 x + 230 y = 257000$ ...........(iii)

Multiplying equation (ii) by $5$ , we get

$276 x + 230 y = 257600$ ...........(iv)

Subtracting equation (iii) from (iv), we get

$x = Rs . 600$

Now, $6 x + 5 y = 5600$ [from (i)]

$\Rightarrow 6 \times 600 + 5 y = 5600 (∵ x = 600)$

$\Rightarrow 5 y = 5600 - 3600$

$\Rightarrow 5 y = 2000$

$\Rightarrow y = 400$

Hence, the C.P. of a saree and C.P. of a sweater are $Rs . 600$ , $Rs . 400$ respectively.

A shopkeeper sells a saree at $8 %$ profit and a sweater at $10 %$ discount, thereby getting a sum of $Rs . 1008$ . 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 that of the sweater.

Important Questions on Pair of Linear Equations in Two Variables

Learn and Prepare for any exam you want !

A shopkeeper sells a saree at 8% profit and a sweater at 10% discount, thereby getting a sum of 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 that of the sweater.

Important Questions on Pair of Linear Equations in Two Variables

Learn and Prepare for any exam you want !

A shopkeeper sells a saree at $8 %$ profit and a sweater at $10 %$ discount, thereby getting a sum of $Rs . 1008$ . 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 that of the sweater.