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The price of sugar having gone down by $10\%$, a consumer can buy $5$ kg more sugar for Rs.$270$. The difference between the original and the reduced price per kg is-A.$62$ paiseB.$60$ paiseC.$75$ paiseD.$53$ paise

Last updated date: 15th Jun 2024
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Hint: Assume the original price to be Rs. x and then subtract the reduced price from the original price to get the new price. Then, since it is given that the consumer buys $5$ kg more sugar for Rs.$270$ at the new price per kg so we can write –
The amount of sugar the consumer buys with original price per kg- the amount of sugar the consumer buys with reduced price per kg=$5$ kg
Solve this equation to get the value of x. Then find the reduced price and subtract it from the original price to get the difference.

Given, the sugar price is reduced by $10\%$ so a consumer buys $5$ kg more for the same price Rs. $270$.
We have to find the difference between the original and the reduced price per kg.
Let the price of $1$ kg of sugar be Rs. x
Then for the price of Rs. $1$we can buy $\dfrac{1}{x}$ kg
Then the amount of sugar consumer buys for Rs. $270$=$\dfrac{{270}}{x}$kg -- (i)
Since the price is reduced by $10\%$ so the new price will be-
$\Rightarrow$ The original price –the reduced price$= x - \dfrac{{10x}}{{100}}$
On solving we get-
$\Rightarrow$ The new price= $\dfrac{{100x - 10x}}{{100}} = \dfrac{{90x}}{{100}} = \dfrac{{9x}}{{10}}$ -- (ii)
Now the amount of sugar the consumer can buy for Rs. $270$=$\dfrac{{270}}{{9x/10}}$kg --- (iii)
Now since the consumer can buy $5$ kg more on the reduced price, then according to question-
$\Rightarrow \dfrac{{270}}{{9x/10}} - \dfrac{{270}}{x} = 5$
On simplifying we get-
$\Rightarrow \dfrac{{270 \times 10}}{{9x}} - \dfrac{{270}}{x} = 5$
On simplifying further we get-
$\Rightarrow \dfrac{{300}}{x} - \dfrac{{270}}{x} = 5$
On taking the LCM of the terms on the left side, we get-
$\Rightarrow \dfrac{{300 - 270}}{x} = 5$
On solving, we get-
$\Rightarrow \dfrac{{30}}{x} = 5$
On exchanging x and $5$, we get-
$\Rightarrow x = \dfrac{{30}}{5}$
O division we get-
$\Rightarrow x = 6$
So the original price is Rs.$6$
Now putting this value in eq.(ii) we get-
The reduced price=$\dfrac{{9 \times 6}}{{10}}$
On solving, we get-
The reduced price=$\dfrac{{27}}{5} = 5.4$
So the difference between the original price and reduced price=$6.00 - 5.40 = 0.60$
The difference between the original price and reduced price=$60$ paise
Hence the correct answer is B.

Note: Here the student may get confused how we got eq. (i).Since for the price of Rs. x we can buy $1$ kg, then for the price of Rs. $1$ we can buy $\dfrac{1}{x}$ kg.
$\Rightarrow$ For price of Rs. $270$, we can buy=$270 \times \dfrac{1}{x}$ kg
Similarly we can find the amount of sugar a consumer can buy with reduced price. Here the student may go wrong if they write the $0.6$ as the answer because we have to find the amount in praise to Rupees.