Question

A shopkeeper sold a saree and a sweater together for ₹1050, thereby making a profit of 10% on a saree and 25% on a sweater. If he had taken a profit of 25% on the saree and 10% on the sweater, he would have got ₹15 more. Find the cost price of each. ​

Answer 1

Question:-

A shopkeeper sold a saree and a sweater together for ₹1050, thereby making a profit of 10% on a saree and 25% on a sweater. If he had taken a profit of 25% on the saree and 10% on the sweater, he would have got ₹15 more. Find the cost price of each.

To Find:-

The cost price of Saree ans sweater.

Solution:-

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

• Profit on saree = 10%

$\therefore \: ₹ S.P. of \: saree = \\ \: \: (1 + \frac{10}{100} ) of \: ₹x = ₹\frac{11}{10} x.$

• Profit of sweater = 25%

$\therefore S.P. \: of \: sweater = \\ \: \: (1 + \frac{25}{100}) \: of \: ₹y \: =₹ \frac{5}{4} \: y.$

As the selling price of both is ₹1050,

$\frac{11}{10}x + \frac{5}{4} y = 1050 \: \: \: \: = > 22x + 25y \\ = 21000 \: \: ...(i)$

Now,profit on saree = 25%,

$\therefore S.P. \: of \: saree \: = \\ (1 + \frac{25}{100} ) \: of \: ₹x \: =₹ \frac{5x}{4} .$

• Profit on sweater = 10%

$\therefore S.P. \: of \: saree \: = \\ (1 + \frac{10}{100} ) \: of \: ₹y \: =₹ \frac{11}{10}y .$

New S.P. of saree and sweater together =

₹1050 + ₹15 = ₹1065,

$\therefore \: \frac{5x}{4} + \frac{11}{10} y = 1065 = >25x + 22y \\ \: \: \: = 21300 \: ...(ii)$

On adding (i) and (ii),we get.

47x + 47y = 42300 => x+y = 900 ...(iii)

Subtracting (i) and (ii),we get

3x – 3y = 300 => x–y = 100 ...(iv)

Adding (iii) and (iv),we get

2x = 1000 => x = 500.

Substituting this value of x in (iii),we get

500 + y = 900 => y = 400.

Hence,the cost price of the saree is ₹500 and the cost price of the sweater is ₹400.

Answer:-

• Cost Price of the saree is = ₹500 and

• cost price of the sweater is = ₹400.

Answer 2

.

$Question:-</p><p></p><p>A shopkeeper sold a saree and a sweater together for ₹1050, thereby making a profit of 10% on a saree and 25% on a sweater. If he had taken a profit of 25% on the saree and 10% on the sweater, he would have got ₹15 more. Find the cost price of each.</p><p></p><p>To Find:-</p><p></p><p>The cost price of Saree ans sweater.</p><p></p><p>Solution:-</p><p></p><p>Let the cost price of the saree be ₹x and the cost price of the sweater be ₹y.</p><p></p><p>Profit on saree = 10%</p><p></p><p>\begin{gathered}\therefore \: ₹ S.P. of \: saree = \\ \: \: (1 + \frac{10}{100} ) of \: ₹x = ₹\frac{11}{10} x.\end{gathered}∴₹S.P.ofsaree=(1+10010)of₹x=₹1011x.</p><p></p><p>Profit of sweater = 25%</p><p></p><p>\begin{gathered}\therefore S.P. \: of \: sweater = \\ \: \: (1 + \frac{25}{100}) \: of \: ₹y \: =₹ \frac{5}{4} \: y.\end{gathered}∴S.P.ofsweater=(1+10025)of₹y=₹45y.</p><p></p><p>As the selling price of both is ₹1050,</p><p></p><p>\begin{gathered}\frac{11}{10}x + \frac{5}{4} y = 1050 \: \: \: \: = > 22x + 25y \\ = 21000 \: \: ...(i)\end{gathered}1011x+45y=1050=>22x+25y=21000...(i)</p><p></p><p>Now,profit on saree = 25%,</p><p></p><p>\begin{gathered}\therefore S.P. \: of \: saree \: = \\ (1 + \frac{25}{100} ) \: of \: ₹x \: =₹ \frac{5x}{4} .\end{gathered}∴S.P.ofsaree=(1+10025)of₹x=₹45x.</p><p></p><p>Profit on sweater = 10%</p><p></p><p>\begin{gathered}\therefore S.P. \: of \: saree \: = \\ (1 + \frac{10}{100} ) \: of \: ₹y \: =₹ \frac{11}{10}y .\end{gathered}∴S.P.ofsaree=(1+10010)of₹y=₹1011y.</p><p></p><p>New S.P. of saree and sweater together =</p><p></p><p>₹1050 + ₹15 = ₹1065,</p><p></p><p>\begin{gathered}\therefore \: \frac{5x}{4} + \frac{11}{10} y = 1065 = > 25x + 22y \\ \: \: \: = 21300 \: ...(ii)\end{gathered}∴45x+1011y=1065=>25x+22y=21300...(ii)</p><p></p><p>On adding (i) and (ii),we get.</p><p></p><p>47x + 47y = 42300 => x+y = 900 ...(iii)</p><p></p><p>Subtracting (i) and (ii),we get</p><p></p><p>3x – 3y = 300 => x–y = 100 ...(iv)</p><p></p><p>Adding (iii) and (iv),we get</p><p></p><p>2x = 1000 => x = 500.</p><p></p><p>Substituting this value of x in (iii),we get</p><p></p><p>500 + y = 900 => y = 400.</p><p></p><p>Hence,the cost price of the saree is ₹500 and the cost price of the sweater is ₹400.</p><p></p><p>Answer:-</p><p></p><p>Cost Price of the saree is = ₹500 and</p><p></p><p>cost price of the sweater is = ₹400</p><p></p><p>$