Question

A shopkeeper sold a saree and a sweater together for ₹1050, thereby making a profit of 25% on the 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

Correct Question :-

A shopkeeper sold a saree and a sweater together for ₹1050, thereby making a profit of 10% on saree and 25% on the 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.

let :-

⟼ The Cost price of Saree = S

⟼ The Cost price of sweater = U

To Find :-

⟼ The Cost price of Saree = ?

⟼ The Cost price of sweater = ?

Solution :-

To calculate the cost price of saree and sweater at first we have to set up equation by Applying formula. Then solve the equation. To set up equation we have to help the given clue in question question.

Calculation for 1st equation :-

A shopkeeper sold a saree and a sweater together for ₹1050, thereby making a profit of on saree 10% and 25% on the sweater.

• SP = ? CP = S, and U , P = 10% and 25%

⟼ SP = (100 + P%)/100 × CP (Formula applied)

⟼ SP of Saree + SP of Sweater = 1050

⟼ (100 + 10)/100 × S + (100 + 25)/100 × U = 1050

⟼ 110S/100 + 125U/100 = 1050

⟼ 1.10S + 1.25U = 1050---------(i)

Calculation for 2nd equation :-

If he had taken a profit of 25% on the saree and 10% on the sweater, he would have got ₹15 more.

• SP = ? CP = S and U. P = 25% and 10%

⟼ SP of Saree + SP of Sweater = 1050 + 15

⟼ (100 + 25)/100 × S + (100 + 10)/100 × U = 1065

⟼ 125S/100 + 110U/100 = 1050

⟼ 1.25S + 1.10U = 1050---------(ii)

In equation (i) multiplying by 1.25 and equation (ii) multiply by 1.10 then subtract.

⟼ 1.375S + 1.5625U = 1312.5------(iii)

⟼ 1.375S + 1.21U = 1171.5--------(iv)

By subtracting equation (iii) and (iv) we get :-]

⟼ 0.3525U = 141 ⟼ U = 400

Putting the value of U = 400 in eq (i) :-]

⟼ 1.10S + 1.25U = 1050

⟼ 1.10S + 1.25(400) = 1050

⟼ 1.10S + 500 = 1050

⟼ 1.10S = 1050 - 500

⟼ 1.10S = 550

⟼ S = 500

Hence,

• The cost price of Saree (s) = ₹ 500
• The cost price of Sweater (u) = ₹ 400

Answer 2

G I V E N :

A shopkeeper sold a saree and a sweater together for ₹1050, thereby making a profit of 25% on the 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.

S O L U T I O N :

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

Profit of the saree = 10%

$\therefore \text{S.P. of the saree} = \frak{ \lgroup 1 + \frac{10}{100} \rgroup } \: \text{of} \: \frak{x = \green{\frac{11}{10}x}}$

Profit of the sweater = 25%

$\therefore \text{S.P. of the sweater} = \frak{ \lgroup 1 + \frac{25}{100} \rgroup} \: \text{of} \: \frak{y = \green{\frac{5}{4}y}}$

As the selling price of both is ₹1050

$\hookrightarrow \frak{ \frac{11}{10}x + \frac{5}{4}y = 1050 } \\ \\ \star \: \underline{ \boxed{ \blue{\frak{22x + 25y = 21000}}}} \qquad \qquad \qquad \lgroup \sf eq(1) \rgroup$

Now, profit of both saree and sweater is ₹1050

$\therefore \text{S.P. of the saree} = \frak{ \lgroup 1 + \frac{25}{100}} \rgroup \: \text{of} \: \frak{x = \orange{\frac{5}{4}x}}$

Profit on sweater = 10%

$\therefore \text{S.P. of the sweater} = \frak{ \lgroup 1 + \frac{10}{100} \rgroup } \: \text{of} \: \frak{y = \ \orange{\frac{11}{10}y}}$

New S.P. of saree and sweater together = ₹1050 + ₹15 = ₹1065

$\therefore \frak{ \frac{5}{4}x + \frac{11}{10}y = 1065 } \\ \\ \underline{ \boxed{ \blue{ \frak{25x + 22y = 21300}}}} \qquad\qquad\qquad \lgroup \sf eq(2) \rgroup$

On adding eq(1) and eq(2) we get

$\mapsto \frak{47x + 47y = 42300} \\ \\ \underline{\boxed{ \frak{ \blue{x + y = 900}}}}\qquad\qquad\qquad \lgroup \sf eq(3)\rgroup$

On subtracting eq(1) from eq(2) we get

$\dashrightarrow \frak{3x - 3y = 300} \\ \\ \underline{\boxed{ \frak{ \blue{x - y = 100}}}}\qquad\qquad\qquad \lgroup \sf eq(4)\rgroup$

Adding eq(3) and eq(4) we get

$\leadsto \frak{2x = 1000} \\ \\ \underline{\boxed{ \frak{ \blue{x = 500}}}}$

Substituting this value of x in eq(3) we get

$\rightharpoonup \frak{500 + y = 900} \\ \\ \underline{\boxed{ \frak{ \blue{y = 400}}}}$

$Hence \rarr \begin{cases}</p><p></p><p> \pink{\text{Cost of saree is } \frak{₹500}}\\</p><p></p><p>\pink{ \text{Cost of sweater is}\frak{₹400}}</p><p></p><p>\end{cases}$