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. Find the cost price of the saree and the list price (price before discount) of the sweater

Answer 1

Let the CP of saree and that of sweater be x and y respectively.

Case 1.

Given that saree is sold at 8% profit

=> SP of saree = x + 8x/100 = 108x/100 

Also, sweater is sold at 10% discount

=> SP of sweater = y - 10y/100 = 9y/10

Given that saree and sweater fetch Rs 1008,

108x/100 + 9y/10 = 1008

=> 108x+90y/100 = 1008

=> 108x + 90y = 100800 => 6x + 5y = 5600 => x = 5600-5y/6 (i)  

Case 2.

Given that saree is sold at 10% profit

SP of saree = x + 10x/00 = 11x/10

Also, sweater is sold at 8% discount

=> SP of sweater = y - 8y/100 = 92y/100 =

Given that saree and sweater fetch Rs 1028,

11x/10 + 92y/100 = 1028

=> 110x+92y/100 = 1028

=> 110x+92y = 102800

Putting value of (i)

110 (5600-5y/6) + 92y = 102800

=> 616000-550y/6 + 92y = 102800

=> 616000-550y-552y/6 = 102800

=> 616000+2y/6 = 102800

=> 616000+2y = 616800

=> 2y = 800

=> y = Rs400

From (i),

x = 5600 - 5*400/6

x = 5600-1200/6

x = 4200/6

=> x = Rs700

Therefore, SP of saree = Rs700

List price of sweater = Rs 400

Answer 2

$\bold{\large{\underline{\underline{\sf{StEp\:by\:stEp\:explanation:}}}}}$

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

Therefore,

$\bold\green{Situation 1 -}$

By selling a saree at 8 % profit and a sweater at 10 % discount, the shopkeeper gets Rs. 1008

⇒ 108x/100 + 90y/100 = 1008

⇒ 27x/25 + 9y/10 = 1008/1

Taking L.C.M. of the denominators and then solving it, we get.

54x + 45y = 50400 _________(1)

$\bold\green{Situation 2 -}$

by selling a saree at 10 % profit and a sweater at 8 % discount, the shopkeeper gets Rs. 1028.

$\sf{ \frac{110x}{100} + \frac{92y}{100} = 1028 }$

$\sf{ \frac{11x}{10} + \frac{23y}{25} = 1028}$

Taking L.C.M. of the denominators and then solving it, we get.

⇒ 55x + 46y = 51400 _______(2)

Now, multiplying the equation (1) by 55 and (2) by 54, we get.

(54x + 45y = 50400)×55

= 2970x + 2475y = 2772000 _____(3)

(55x + 46y = 51400)×54

= 2970x + 2484y = 2775600 _____(4)

Now, subtracting (3) from (4), we get.

2970x + 2484y = 2775600

2970x + 2475y = 2772000

. - - - ___________________________

. 9y = 3600

___________________________

⇒ 9y = 3600

y = 3600/9

y = 400

Putting the value of y = 400 in (1), we get.

54x + 45y = 50400

54x + (45 × 400) = 50400

54x + 18000 = 50400

54x = 50400 - 18000

54x = 32400

.

x = 600

So, the cost price of a saree is Rs. 600 and the list price of a sweater is Rs. 400.