We get 2 kg of pure butter less in Rs. 960 i | vedclass

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Question

(A) Let the original price of pure butter be $x$ Rs. per $kg$.The quantity of butter purchased for Rs. $960$ at the original price is $\frac{960}{x} \

Vedclass · Accepted Answer

$120$

Vedclass · Answer

(A) Let the original price of pure butter be $x$ Rs. per $kg$.The quantity of butter purchased for Rs. $960$ at the original price is $\frac{960}{x} \ kg$.When the price increases by Rs. $40$ per $kg$,the new price becomes $(x + 40)$ Rs. per $kg$.The quantity of butter purchased for Rs. $960$ at the new price is $\frac{960}{x + 40} \ kg$.According to the problem,the difference in quantity is $2 \ kg$:$\frac{960}{x} - \frac{960}{x + 40} = 2$Divide by $2$:$\frac{480}{x} - \frac{480}{x + 40} = 1$$480(x + 40) - 480x = x(x + 40)$$480x + 19200 - 480x = x^2 + 40x$$x^2 + 40x - 19200 = 0$Solving the quadratic equation using the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$:$x = \frac{-40 \pm \sqrt{1600 - 4(1)(-19200)}}{2}$$x = \frac{-40 \pm \sqrt{1600 + 76800}}{2} = \frac{-40 \pm \sqrt{78400}}{2} = \frac{-40 \pm 280}{2}$Since price cannot be negative,$x = \frac{240}{2} = 120$.Thus,the original price is Rs. $120$ per $kg$.

We get $2 \ kg$ of pure butter less in Rs. $960$ if the price of pure butter increases by Rs. $40$ per $kg$. Find the original price of pure butter per kilogram.

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