housewife per used to spend rupees 120 per month on the purchase of wheat at prevailing price when the price Rose by rupees 2 per kg she found that for the same amount she could purchase 2 kg less find the new price per kg of the weight
Answers
Let us assume she used to by x kg of wheat with 120 rupees. This means, and I'm gonna use unitary method here, so watch carefully:
Initial cost of x kg of wheat = 120
Initial cost of 1 kg of wheat = 120/x
New cost of 1 kg wheat = 2 + old cost = 2 + 120/x
This means that spending the same amount of money (120 rupees) now bought her 2 kg less amount of wheat. Which can be written as:
(2 + 120/x) (x -2) = 120
(2x + 120)(x-2) = 120x
2x² - 4x + 120x -240 = 120x
2x² - 4x - 240 = 0
x² - 2x - 120 = 0
(x+10)(x-12) = 0
x = -10 or x = 12
Since weight can not be negative, so x = 12.
Check: If she bought 12 kg wheat @ 120 Cost of 1 kg wheat = 10 rupees.
When cost increased by 2 rupees, i.e. new cost = 12 rupees, she could buy 120/12 = 10 kg of wheat which is 2 kg less than what she originally bought.
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