Question

A tradesman sold an article at loss 20%.had he sold it for Rs 100 more to have gained 5% . find CP

Answer 1

If the tradesman sold an article at loss 20%
and since
Loss% = [ ( CP - SP ) * 100 ] / CP
20 = [ ( CP - SP ) * 100 ] / CP
20 * CP = ( CP - SP ) * 100
( 20 * CP ) / 100 = CP - SP
( CP / 5 ) - CP = -SP
SP = CP - ( CP / 5 )
SP = 0.8 * CP (1)

If had he sold it for Rs 100 more to have gained 5% then
Gain% = [ ( (SP+100) - CP ) * 100 ] / CP
5 = [ ( SP +100 - CP ) * 100 ] / CP
5 * CP = ( SP + 100 - CP ) * 100
( 5 * CP ) / 100 = SP + 100 - CP
( CP / 20 ) + CP = SP + 100
SP + 100 = CP + ( CP / 20 )
SP = 1.05 * CP - 100 (2)

Now equating equation (1) and (2)
1.05 * CP - 100 = 0.8 * CP
1.05 * CP - 0.8 * CP = 100
0.25 * CP = 100
CP = 100 / 0.25
CP = 400

Answer 2

Let C.P be x,
Then,(100+5 of x)-(100-20 of x)
=100 or 25% of x = 100
Therefore, x/4 = 100
                 x = 100 X (into) 4
                 x = 400
Therefore, C.P = 400 rupees
  

                                                                   (OR)

Let Cost Price of the article be Rs.K. By selling at 20% loss, tradesman sells at (100-20)% of CP,i.e., (80/100)xK = 0.8K. If the price is increase by Rs.100, then selling price becomes = (0.8K + 100). He gains 5% with SP = (0.8K+100) and CP = K ==> Profit = SP - CP = (0.8K+100) - K = (100 - 0.2K). Now Profit (100 - 0.2K) = (5/100) of CP = 0.05xK ==> 0.25K = 100 or Cost Price K = 100/0.25 = 400