Question

a trademan sold an article at a loss of 20%.Had he sold it for 100 rs more ,he would gain 5%.find cp of article

Answer 1

Let the Cost Price of article = CP
He sold it at 20% loss, SP = CP×(100-20 / 100) = 0.8CP

If he had sold it at 5% gain, SP = CP×(100+5 / 100) = 1.05CP
This is Rs. 100 more than 0.8CP

1.05CP - 0.8CP = 100
⇒ 0.25CP = 100
⇒ CP = 100/0.25
⇒ CP = Rs. 400

CP of article is Rs. 400

Answer 2

Let the C.P Of the article be x Rs
with a loss of 20% S.P = C.P - 20% of C.P
S.P = x - (20/100)* x
      = x - x/5
      =(5x - x)/5
      =4x/5
∴S.P = 4x/5 Rs
When S.P is increased by Rs 100 there is a gain of 5%
∴S.P + 100 = C.P+5% of C.P
⇒4x/5 + 100 = x + (5/100)* x
⇒4x/5 - x - x/20 = - 100
⇒(16x - 20x - x)/20 = - 100
⇒ -- 5x = -- 100* 20
⇒ --5x = -- 2000
⇒  x  =  --2000/ --5
∴   x =  400
∴C.P = 400 Rs.