Question

The price of wheat falls by 16%. By what percentage a person can increase the consumption of wheat so that his overall budget does not change?
A. 16%
B. 18%
C. \[18.5\% \]
D. 19%

Answer 1

Hint: We will first consider the given data that is the price of the wheat falls by 16% and let it as \[R\]. We have to find the percentage increase in the consumption of wheat. So, we will divide the given percentage of the price of wheat that is \[R\] by \[100 - R\] and multiply it with 100 to convert it into percentage and thus get the desired result.

Complete step by step answer:

We will first let the given fall in price of wheat as \[R\].
That is \[R = 16\% \]
Now, as we have to find the increase in the consumption of wheat so, we will use the formula, \[I = \left[ {\dfrac{R}{{100 - R}} \times 100} \right]\% \] where \[I\] denotes the increase in consumption.
Thus, we will substitute the values in the above formula,
Hence, we get,
\[
   \Rightarrow I = \left[ {\dfrac{{16}}{{100 - 16}} \times 100} \right]\% \\
   \Rightarrow I = \dfrac{{16}}{{84}} \times 100 \\
 \]
Now, we will further simplify the above expression and determine the percentage of increase in the consumption of wheat.
\[
   \Rightarrow I = \dfrac{{400}}{{21}}\% \\
   \Rightarrow I = 19.04\% \\
   \Rightarrow I \approx 19\% \\
 \]
Thus, we can conclude that the increase in the consumption of wheat is \[19\% \]
Hence, option D is correct.

Note: As we have found the increase in percentage so we have divided the given price of wheat falls by \[100 - \] the price of wheat falls. Whenever we have to find the percentage, we need to multiply the expression by 100. At last we round off the decimal and convert the percentage in whole number form. Do not convert the percentage in any other form. Perform the calculations properly.