Question

If the price of wheat is increased by $30\%$. By what $\%$ should a family decrease the consumption of wheat, so there is no change in the expenditure.

Answer 1

Hint: In order to solve this problem, we need to assume a base price and then continue with the calculation. We can calculate the exact increase in the price with the assumed price and then calculate the reduction to compensate for the increase with respect to the new price of the product.

Complete step-by-step solution:
We need to find an increase in the expenditure on this account in account to the condition that the price has increased by $30\%$.
We can solve this by assuming a base price.
We can take any amount because eventually, we have asked for a relative increase so the result would be the same.
We can assume that let the original price be $\text{Rs.}100$.
Now we have the condition that the price has increased by $30\%$.
We need to find $30\%$ of $\text{Rs.}100$.
Therefore, $30\%$ of $100 = \dfrac{30}{100}\times 100=30$.
Adding Rs. $30$ to Rs. $100$ we get, $100+30 = \text{Rs.}130$.
Hence, the increased price is $\text{Rs.}130$.
In order to not increase the expenditure, the family needs to be the reduction.
The reduction has by the same amount that is $\text{Rs.}30$.
Therefore, now the reduction of $30$ out of the new price of $\text{Rs.}130$.
We need to calculate the percentage therefore; we need to multiply the ratio by $\text{Rs.}100$.
Therefore, the percentage of reduction = $\dfrac{30}{130}\times 100=23.077\%$.

Note: We need to understand that the reduction is with respect to the new price and not by the base price of $\text{Rs.}100$. The new price is $\text{Rs.}130$, the ratio is taken with respect to 130. Also, in the beginning, we can imagine any value for the base price, because we will eventually take the ratio and the answer would remain the same.