Question

The price of sugar is reduced by \[2\% \]. How many kg of sugar now can be bought for the money, which was sufficient to buy 49 kg of sugar earlier?
A. 1 kg less
B. 1 kg more
C. 2 kg more
D. 2 kg less

Answer 1

Hint: First, we will first assume the value of the price with any variable. Then we will find the new price of the sugar and the total amount of sugar for the obtained price.
Apply these, and then use the given conditions to find the required value.

Complete step-by-step solution
We are given that the price of sugar is reduced by \[2\% \].

Let us assume that the price of sugar is \[x\].

We will now calculate the price for 49 kg in terms of \[x\].

\[49 \times x = 49x\]

We will now find the new price of sugar by subtracting the reduction of 2 percent from the total.

\[
  \left( {1 - \dfrac{2}{{100}}} \right)x = \left( {1 - 0.02} \right)x \\
   = 0.98x \\
 \]

We will now calculate the total amount of sugar for a new price by dividing the 49 kg of sugar by the new price sugar.

\[
  \dfrac{{49x}}{{0.98x}} = \dfrac{{4900}}{{98}} \\
   = 50{\text{ kg}} \\
 \]

Thus, the total amount of sugar for a new price is 50 kg.

Subtracting the 49 kg of sugar from the total amount of sugar for a new price, we get

\[
  50{\text{ kg}} - 49{\text{ kg}} = \left( {50 - 49} \right){\text{kg}} \\
   = 1{\text{ kg}} \\
 \]
Thus, 1 kg more can be bought with a new price.

Therefore, 1 kg of sugar now is bought for the money, which was sufficient to buy 49 kg of sugar earlier.

Hence, the option B is correct.

Note: In solving these types of questions, we have to consider in terms of some unknown variable then deal with the problem in the same variable. Students have to calculate the total amount of sugar for a new price by dividing the 49 kg of sugar by the new price sugar. We must note that we have to find the amount of sugar for a new price by subtracting the old amount from the new amount of sugar.