a shopkeeper sold an article for Rs. 39 and gained as much percent as the cost price. Find the cost price.
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47
Let the cost price = x
Amount gained = 39 - x
Amount gained as a percentage = (39 - x)/x * 100
This percentage = cost price = x
So,
(39 - x)/x * 100 = x
x² + 100x - 3900 = 0
x² + 130x - 30 x - 3900 = 0
x(x + 130) - 30(x + 130) = 0
(x - 30)(x + 130) = 0
x = 30 or -130
Take x = 30
The cost price = Rs. 30
Amount gained = 39 - x
Amount gained as a percentage = (39 - x)/x * 100
This percentage = cost price = x
So,
(39 - x)/x * 100 = x
x² + 100x - 3900 = 0
x² + 130x - 30 x - 3900 = 0
x(x + 130) - 30(x + 130) = 0
(x - 30)(x + 130) = 0
x = 30 or -130
Take x = 30
The cost price = Rs. 30
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