Question

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.$62$ paise
B.$60$ paise
C.$75$ paise
D.$53$ paise

Answer 1

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.

Complete step-by-step answer:
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.