Question

The price of rice is reduced by 2%. How many kilograms of rice can now be bought for the money which is sufficient to buy 49 kg of rice earlier?
\[\begin{align}
  & (A)\text{ }50kg \\
 & (B)\text{ 55 kg} \\
 & \text{(C) 52 kg} \\
 & \text{(D) 60 kg} \\
\end{align}\]

Answer 1

Hint: We should assume the price of rice as p. We should decrease the price of rice by 2% by subtracting 2% of p from p. Now, we have to calculate the total price sufficient to buy 49 kilograms of rice. For which, first we have to calculate the money required to buy x kilograms at the reduced price. The price required to buy x kilograms at the reduced price is equal to the price required to buy 49 kilograms of rice at initial price. In this way we should find the number of kilograms of rice that can be bought for the money which is sufficient to buy 49 kg of rice earlier.

Complete step-by-step answer:
Before solving the question, we should understand the concept of percentage. We know that the p% of a number x is equal to \[x\left( \dfrac{p}{100} \right)\]. Assume the old price of 1 kilogram of rice is p. It is given that the price of rice is reduced by 2%.
So, we can write
New price = Old price \[-\left( \dfrac{2}{100} \right)\] (old price)
\[\Rightarrow \]New price =p \[-\left( \dfrac{2}{100} \right)\] (p)
\[\Rightarrow \]New price\[=\dfrac{98p}{100}\]
\[\Rightarrow \]New price\[=\dfrac{49p}{50}.....(1)\]
From equation (1),
It is clear that if old price of 1 kilogram of rice is p then new price of 1 kilogram of rice is \[\dfrac{49p}{50}.\]
If the old price of one kilogram of rice is p then the old price of n kilograms of rice is np.
\[\begin{align}
  & 1\to p \\
 & n\to np \\
\end{align}\]
If the new price of one kilogram of rice is \[\dfrac{49p}{50}\] then we will assume the new price of x kilograms of rice is equal to np.
\[\begin{align}
  & 1\to \dfrac{49p}{50} \\
 & x\to np \\
\end{align}\]
By using criss-cross method,
\[\begin{align}
  & (1)(np)=(x)\left( \dfrac{49p}{50} \right) \\
 & \Rightarrow np=\dfrac{49px}{50}......(1) \\
\end{align}\]
Now we will divide the equation (1) with p on both sides.
\[\begin{align}
  & \Rightarrow n=\dfrac{49x}{50} \\
 & \Rightarrow x=\dfrac{50n}{49}.....(2) \\
\end{align}\]
So, we get the new price of \[\dfrac{50n}{49}\] kilograms of rice is np.
 \[\dfrac{50n}{49}\to np\]
By using criss-cross method,
\[50n\to 49np\]
So, the new price of 50n kilograms of rice is 49np.
\[\begin{align}
  & 50n\to 49np \\
 & 50\to 49p \\
\end{align}\]
Then the new price of 50 kilograms of rice is 49p.
We know that the old price of 49 kilograms rice is 49p.
Hence, we get that 50 kilograms of rice can now be bought for the money which is sufficient to buy 49 kg of rice earlier.
Hence, option A is correct.

Note: We should be careful while solving the problem. We should identify the given data in the question and we should also identify which data is required to find in the question. In this question, we are given that the price was reduced by 2%. If it was given that price was reduced to 2%, the new price would have been just 2% of p. So it is important to note the word after ‘reduced’ also.