Question

a shopkeeper sells a saree at 8%profit and a sweater at 10%discount thereby getting a sum rupees 1008 if she had sold the saree at 10% profit and the sweater at discount she would have got rupees 1028 find the cost of saree and list price of the sweater

Answer 1

Solution :-

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

Therefore,

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)

Situation 2 -

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

⇒ 110x/100 + 92y/100 = 1028

⇒ 11x/10 + 23y/25 = 1028/1

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 = 32400/54

x = 600

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