.ch-Problems on Simultaneous Linear Equations:

24. A shopkeeper sells a table at 8% profit and a chair at 10% discount, thereby getting Rs. 1008. If he had sold the table at 10% profit and chair at 8% discount, he would have got Rs. 20 more. Find the cost price of the table and the list price of the chair. 
 

Let the CP of table and that of chair be x and y respectively.

Case 1.

Given that table is sold at 8% profit

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

Also, chair is sold at 10% discount

=> SP of chair = y - 10y/100 = 9y/10

Given that table and chair 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 table is sold at 10% profit

SP of table = x + 10x/00 = 11x/10

Also, chair is sold at 8% discount

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

Given that table and chair 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 table = Rs700

List price of chair = Rs 400

​For remaining queries, please post them in a different thread to get rapid assistance from our experts.