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.

M L Aggarwal Solutions for Chapter: Pair of Linear Equations in Two Variables, Exercise 8: Higher Order Thinking Skills (HOTS)

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Chapter: Pair of Linear Equations in Two Variables, Exercise 8: Higher Order Thinking Skills (HOTS)

Questions from M L Aggarwal Solutions for Chapter: Pair of Linear Equations in Two Variables, Exercise 8: Higher Order Thinking Skills (HOTS) with Hints & Solutions

Learn and Prepare for any exam you want !