Name: Equations Reducible to a Pair of Linear Equations
Uploaded: 2019-07-19
Duration: 4 min 9 s
Description: Some equations may be in a form that can be reduced to a linear equation through substitution. Do you want to explore how this can be done? Watch the video t...

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. $1028$ then find the cost of the saree and the list price (price before discounted) of the sweater.

Accepted Answer

Let the cost price of the s $10 %$ aree and the list price of the sweater be Rs. $x$ and Rs. $1008$ , respectively.

Case $I$ sells a saree at $8 %$ $p r o f i t + S e l l s a s w e a t e r a t d i s c o u n t = R s,$

$\Rightarrow (100 + 8) %$ of $x + (100 - 10) %$ of $y = 1008$

$\Rightarrow 108 % o f x + 90 % o f y = 1008$

$\Rightarrow 1.08 x + 0.9 y = 1008$ $. . . (i)$

Case $I I$ Sold the saree at $10 %$ profit $+$ Sold the sweater at $8 %$ discount $=$ Rs. $1028$

$\Rightarrow (100 + 10) %$ of $x + (100 - 8) %$ of $y = 1028$

$\Rightarrow 110 %$ of $x + 92 % o f y = 1028$

$\Rightarrow 1.1 x + 0.92 y = 1028$ $. . . (i i)$

On putting the value of $y$ from Eq. $(i)$ into Eq. $(i i)$ , we get

$1 .1 x + 0 .92 (\frac{1008 - 1.08 x}{0 .9}) = 1028$

$\Rightarrow 1 .1 \times 0 .9 x + 927 .36 - 0.9936 x = 1028 \times 0 .9$

$\Rightarrow 0 .99 x - 0.9936 x = 925.2 - 927 .36$

$\Rightarrow - 0 .0036 x = - 2 .16$

$x = \frac{2.16}{0.0036} = 600$

On putting the value of $x$ in Eq. $(i)$ , we get

$1.08 \times 600 + 0.9 y = 1008$

$\Rightarrow 108 \times 6 + 0 .9 y = 1008$

$\Rightarrow 0 .9 y = 1008 - 648$

$\Rightarrow 0 .9 y = 360$

$\Rightarrow y = \frac{360}{0 .9} = 400$

Hence, the cost price of the saree and the list price (price before discount) of the sweater are Rs. $600$ and Rs. $400$ , respectively.

Important Questions on Pair of Linear Equations in Two Variables

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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 then find the cost of the saree and the list price (price before discounted) of the sweater.

Important Questions on Pair of Linear Equations in Two Variables

Learn and Prepare for any exam you want !