Question

a watch was sold by a shopkeeper at a gain of 5% . if he had sold it for 1650 less , he would have suffered a loss of 5%. find the CP

Answer 1

let cp of the article = x
at 5% gain sp of article = x + (5/100)x = 1.05x
at 5% loss sp of article = x - (5/100)x = 0.95x
given that 1.05x - 0.95x = 1650
 ⇔0.1x = 1650
⇔ x = 1650/0.1
 ⇔x = Rs. 16500

Answer 2

let cp of watch=Rs x
profit=5%
sp=(100+p/100)×cp
=(100+5/100)×x
=105x/100
when loss of 5%
sp=(100-5/100)×x
=95x/100
105x/100-1650=95x/100
105x/100-95x/100=1650
10x/100=1650
10x=165000
x=16500
CP=Rs 16500


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