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# A reduction of 10% in the price of sugar enables a housewife to buy 6.2 kg more for Rs. 1116. Find the reduced price per kg.

Hint: For solving this question we will use the concept of percentage and make equations stepwise as per the given conditions and then calculate the correct answer.

Given:
If the price of sugar is reduced by 10% then, we can buy 6.2 kg more sugar for Rs. 1116.
First, we will understand the concept of percentage and then we will proceed further.
Let us consider a number $N$ .

Then, $y\%$ of $N$ = $\dfrac{y}{100}\times N$.
If $N$ decreases by $y\%$ . Then, $N$ will become $N-\dfrac{y}{100}\times N=N\times \left( 1-\dfrac{y}{100} \right)$.
We will directly use the formula from the above equation for solving this question.
In our question $y=10$ . Then, $N$ will become $N-\dfrac{y}{100}\times N=N\times \left( 1-\dfrac{10}{100} \right)=N\times 0.9$.
From the above calculation, if any number is increased 10% then, it’s final value will be 0.9 times the initial value. We will use this result directly to solve this question.
Let the original price of sugar is Rs. $x$ per kg.
We can buy 1 kg of sugar with Rs. $x$. Then, with Rs. 1 we can buy $\dfrac{1}{x}$ kg of sugar.
Then, the amount of sugar we can buy with Rs. 1116 $={{Y}_{Initial}}=\dfrac{1116}{x}$ kg.

Now, the price is reduced by 10%. Then,
Reduced price of sugar per kg in Rs. $=0.9x$.
Then, the final amount of sugar we can buy with Rs. 1116 $={{Y}_{Final}}=\dfrac{1116}{0.9x}=\dfrac{1240}{x}$ kg.
Now, as per the data given in the question. When the price per kg is reduced by 10% then, we can buy 6.2 kg more sugar for Rs. 1116.

Then,
Amount of sugar with Rs. 1116 on reduced price = 6.2 kg + Amount of sugar with Rs. 1116 on the original price.
Now, substitute ${{Y}_{Initial}}=\dfrac{1116}{x}$ and ${{Y}_{Final}}=\dfrac{1240}{x}$ in the above equation. Then,
\begin{align} & {{Y}_{Final}}=6.2+{{Y}_{Initial}} \\ & \Rightarrow \dfrac{1240}{x}=6.2+\dfrac{1116}{x} \\ & \Rightarrow \dfrac{1240}{x}-\dfrac{1116}{x}=6.2 \\ & \Rightarrow \dfrac{1240-1116}{x}=6.2 \\ & \Rightarrow \dfrac{124}{x}=6.2 \\ & \Rightarrow \dfrac{x}{124}=\dfrac{1}{6.2} \\ & \Rightarrow x=\dfrac{124}{6.2}=20 \\ & \Rightarrow x=20 \\ \end{align}

Thus, the original price of sugar will be Rs. 20 per kg.
In the question the reduced price of the sugar per kg is asked. Then,
As the price is reduced by 10% so, reduced price per kg $=0.9x=0.9\times 20=18$ .
Thus, the reduced price per kg is Rs. 18.

Note: Here, a student must apply the percentage concept accurately and proceed step by step to find the answer for the question. Moreover, in the question, reduced price is asked so, be careful while giving the final answer.