A shopkeeper sold a saree and a sweeter together for Rs. 1050, thereby making a profit of 10% on the saree and 25% on the sweater. If he has taken a profit of 25% on the saree and 10% on the sweater, he would have got Rs. 15 more. Find CP of each.. Created by SnowFlxwer.

A shopkeeper sold a saree and a sweeter together for Rs. 1050, thereby making a profit of 10% on the

[tex]\large\underline\color{grey}{\sf{Solution\: : - }}[/tex]

Let the cost of the saree be 'x' and the cost price of sweater be 'y'.

By selling a saree at 10% profit and a sweater at 25% Profit , the shopkeeper gets Rs.1050

[tex]\:\:\:\:\:\:\:\:\:\:[/tex] Profit on Saree : 10%

[tex]\:\:\:\:\:\:\:\:\:\:[/tex] S.P of Saree : [tex]\sf{1 + \dfrac{10}{100}}[/tex] of Rs.x

[tex]\:\:\:\:\:\:\:\:\:\:[/tex][tex]\hookrightarrow[/tex] [tex]\sf{x : -\dfrac{11}{10}}[/tex]

[tex]\:\:\:\:\:\:\:\:\:\:[/tex] Profit on Sweater : 25%

[tex]\:\:\:\:\:\:\:\:\:\:[/tex] S.P of Sweater: [tex]\sf{1 + \dfrac{25}{100}}[/tex] of Rs.y

[tex]\:\:\:\:\:\:\:\:\:\:[/tex][tex]\hookrightarrow[/tex] [tex]\sf{y : -\dfrac{5}{4}}[/tex]

Now the selling price of both is ₹1050.

[tex]\:\:\:\:\:\:\:\:\:\:[/tex] [tex]\sf{\dfrac{11}{10}x + \dfrac{5}{4} y = 1050 }[/tex]

[tex]\:\:\:\:\:\:\:\:\:\:[/tex] [tex]\sf{22x + 25y = 21000 }[/tex] [tex]\:\:\:\:\:\:\:\:\:\:[/tex]...(i)

[tex]\:\:\:\:\:\:\:\:\:\:[/tex] Profit on Saree : 25%

[tex]\:\:\:\:\:\:\:\:\:\:[/tex] S.P of Saree : [tex]\sf{1 + \dfrac{25}{100}}[/tex] of Rs.x

[tex]\:\:\:\:\:\:\:\:\:\:[/tex][tex]\hookrightarrow[/tex] [tex]\sf{x : -\dfrac{5}{4}}[/tex]

[tex]\:\:\:\:\:\:\:\:\:\:[/tex] Profit on Sweater : 10%

[tex]\:\:\:\:\:\:\:\:\:\:[/tex] S.P of Sweater: [tex]\sf{1 + \dfrac{10}{100}}[/tex] of Rs.y

[tex]\:\:\:\:\:\:\:\:\:\:[/tex][tex]\hookrightarrow[/tex] [tex]\sf{y : -\dfrac{11}{10}}[/tex]

Now, by taking a profit of 25% on the saree and 10% on the sweater :

New S.P of saree and sweater together :

[tex]\:\:\:\:\:\:\:\:\:\:[/tex][tex]\hookrightarrow[/tex]1050 + 15 : - 1065

[tex]\:\:\:\:\:\:\:\:\:\:[/tex] [tex]\sf{\dfrac{5x}{4}+ \dfrac{11}{10} y = 1065 }[/tex]

[tex]\:\:\:\:\:\:\:\:\:\:[/tex] [tex]\sf{25x + 22y = 21300 }[/tex]..(ii)

On Adding (i) and (ii) , We get :

[tex]\:\:\:\:\:\:\:\:\:\:[/tex] [tex]\hookrightarrow[/tex] [tex]\sf{47x + 47y = 42300}[/tex]

[tex]\:\:\:\:\:\:\:\:\:\:[/tex] [tex]\hookrightarrow[/tex] [tex]\sf{x + y = 900}[/tex]...(iii)

On Subtracting (i) from (ii) , We get :

[tex]\:\:\:\:\:\:\:\:\:\:[/tex] [tex]\hookrightarrow[/tex] [tex]\sf{3x - 3y = 300}[/tex]

[tex]\:\:\:\:\:\:\:\:\:\:[/tex] [tex]\hookrightarrow[/tex] [tex]\sf{x - y = 100}[/tex]...(iv)

On Adding (iii) and (iv) , We get :

[tex]\:\:\:\:\:\:\:\:\:\:[/tex] [tex]\hookrightarrow[/tex] [tex]\sf{2x + 1000 = x }[/tex]

[tex]\:\:\:\:\:\:\:\:\:\:[/tex] [tex]\hookrightarrow[/tex] [tex]\sf{x = 500}[/tex]...

Now , by substituting this value of x in (iii) :

[tex]\:\:\:\:\:\:\:\:\:\:[/tex] [tex]\sf{500 + y = 900 }[/tex]

[tex]\:\:\:\:\:\:\:\:\:\:[/tex] [tex]\sf{900 = y = 500}[/tex]

Hence ,the cost price of saree is Rs. 900 and the cost of sweater is Rs. 500