Question

A person gains Rs. 357 on selling a table at 13% gain and a chair at 6% gain. If he sells the table at 15% gain and the chair 8% loss, he gains Rs. 203. What is the actual cost of the chair ?

Answer 1

Let us assume that , the cost of table be Rs.x and chair is Rs.y.

 

Case 1) :- Table at 13% gain and chair at 6% gain .

 

So,

→ Total gain = gain in table + gain in chair,

→ 357 = (13/100) of x + (6/100) of y

→ 357 = (13x/100) + (6y/100)

→ 357*100 = 13x + 6y

→ 13x + 6y = 35700 ------------- Eqn.(1)

 

 

Case 2) :- Table at 15% gain and chair at 8% loss.

 

So,

→ Total gain = gain in table - loss in chair,

→ 203 = (15/100) of x - (8/100) of y

→ 203 = (15x/100) - (8y/100)

→ 203*100 = 15x - 8y

→ 15x - 8y = 20300 ------------- Eqn.(2)

 

Multiply Eqn.(1) by 4 and Eqn.(2) by 3 and adding them,

→ 4(13x + 6y) + 3(15x - 8y) = 4*35700 + 3*20300

→ 52x + 24y + 45x - 24y = 142800 + 60900

→ 97x = 203700

dividing both sides by 97,

→ x = Rs.2100 .

 

Putting value of x in Eqn.(2) now,

→ 15*2100 - 8y = 20300

→ 8y = 31500 - 20300

→ 8y = 11200

dividing both sides by 8,

→ y = Rs.1400 (Ans.)