Question

By a reduction of Rs. 1 per kg in the sugar, Mohan can buy one kg sugar more for Rs. 56. Find the original price of sugar per kg.

Answer 1

Let the original price of 1 kg sugar = Rs. x

Total money = Rs. 56
Quantity of sugar bought for Rs. 56 = $\left(\frac{56}{x}\right)\mathrm{kg}$
Let the reduced price of 1 kg sugar = Rs. (x - 1)


Total money = Rs. 56
Quantity of sugar bought for Rs. 56 = $\left(\frac{56}{x-1}\right)\mathrm{kg}$

According to question,
$$\begin{gathered} \frac{56}{x-1}-\frac{56}{x}=1 \\ \Rightarrow \frac{56x-56(x-1)}{x(x-1)}=1 \\ \Rightarrow \frac{56x-56x+56}{x^2-x}=1 \\ \Rightarrow x^2-x-56=0 \\ \Rightarrow x^2-8x+7x-56=0 \\ \Rightarrow x(x-8)+7(x-8)=0 \\ \Rightarrow (x-8)(x+7)=0 \\ \Rightarrow x-8=0orx+7=0 \\ \Rightarrow x=8orx=-7\left(\mathrm{rejected}\right) \\ \mathrm{so}\mathrm{original}\mathrm{price}\mathrm{of}1\mathrm{kg}\mathrm{sugar}=\mathrm{Rs}.8.00 \end{gathered}$$