a housewife 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 the same amount should purchase 2 kg less. Find the new price per kg of the wheat.

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Solution

Dear Student,

Let price of wheat=Rs x

And quantity of wheat=y

Now, Budget=Price×Quantity
⇒120=xy
⇒x=120/y ....(1)
According to question:(x+2(y−2)=120
⇒xy−2x+2y−4=120 ..(2)

Substitute value of y and xy in equation(2),
we have,
120−(2×120/y)+2y−4=120
⇒−2×120/y+2y=4
⇒−120/y+y=2
⇒y^2−2y−120=0
⇒(y+10)(y−12)=0
⇒y=−10 and y=12
Quantity can't be negative
so y=12
Substitute value of y in equation(1),
x=120/12=10
So, new price=x+2
=10+2=12
Hence new price of the wheat is Rs 12/kg.
Hope this would help.

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