Question

# A rise of 25 % in the price of sugar, compels a man to buy 5 kg sugar less for Rs. 200. Calculate the original price per kg of the sugar.

Hint: In the above question, we will first assume the original cost of the sugar to be a variable. Also, we will assume the original amount of sugar to be another variable. Since, the total cost remains the same, we will equate the original cost to the new cost.

Let us suppose the original cost of the sugar to be Rs. C/kg.
Since it is given that there is a rise of 25 % in the price of sugar.
So the new cost is equal to 25 % increment in the original cost.
New cost,
\begin{align} & =\left( C+25\%\times C \right) \\ & =C+\dfrac{25}{100}\times C \\ & =C+\dfrac{1}{4}C \\ & =\dfrac{5}{4}C \\ \end{align}
Now let us suppose the original amount of sugar bought be x kg.
As it is given that the man buys 5 kg sugar less.
Then, new amount of sugar $=(x-5)kg$.
Also, original cost of sugar $=Rs.\left( C\times x \right)$.
New cost of sugar = new amount $\times$ new cost
\begin{align} & =(x-5)\times \dfrac{5}{4}C \\ & =Rs.\dfrac{5}{4}C(x-5) \\ \end{align}
Since we know that the total cost remains the same, we have as follows:
$C\times x=\dfrac{5}{4}C(x-5)$.
We also have been given that the total cost is Rs. 200.
$C\times x=\dfrac{5}{4}C(x-5)=200....(1)$
Now considering $C\times x=\dfrac{5}{4}C(x-5)$.
$\Rightarrow Cx=\dfrac{5}{4}Cx-\dfrac{25}{4}C$.
By taking $\dfrac{25}{4}C$ to the left hand side of the equal sign, we get as follows:
$Cx+\dfrac{25}{4}C=\dfrac{5}{4}Cx$
Again, by taking the term ‘Cx’ to the right hand side of the equal sign, we get as follows:
\begin{align} & \dfrac{25}{4}C=\dfrac{5}{4}Cx-Cx \\ & \dfrac{25}{4}C=Cx\left( \dfrac{5}{4}-1 \right) \\ & \dfrac{25}{4}C=Cx\left( \dfrac{5-4}{4} \right) \\ & \dfrac{25}{4}C=Cx\times \dfrac{1}{4} \\ \end{align}
On multiplying the above equation by ‘4’, we get as follows:
\begin{align} & 4\times \dfrac{25}{4}C=\dfrac{Cx}{4}\times 4 \\ & 25C=Cx \\ \end{align}
We know that the value of $Cx=200$ from equation (1).
So, by substituting the value of $Cx=200$ in the above equation, we get as follows:
\begin{align} & 25C=Cx \\ & 25C=200 \\ & C=\dfrac{200}{25} \\ & C=8 \\ \end{align}
Therefore, the original price per kg of the sugar is equal to Rs. 8.

Note: Be careful while doing calculation and take care of the sign while solving the equation. We can also solve this question by considering the other two expressions from the equation (1).