Question

Price of a product has increased 18%. In which ratio the price should be decreased such that the price drops down to initial price?

Answer 1

Hint: We start solving the problem by assigning the variable for the original price of the product. We then find the price after increasing it by 18% by using the fact that a% of b is $\dfrac{a}{100}\times b$. We then assume the ratio at which the new price can be reduced to its and price. We multiply the new price with the ratio and equate it with the original price. After finding the value of this assumed ratio, we subtract it from 1 in order to get the ratio that is decreased.

Complete step-by-step answer:
According to the problem, we are given that the price of a product is increased by 18% and we need to find the ratio at which we need to decrease the price in order to get it to its initial price.
Let us assume the original price of the product is ‘x’.
Now, this price has increased by 18%. So, the new price is $\left( 100+18 \right)\%=118\%$ of the price ‘x’.
We know that a% of b is defined as $\dfrac{a}{100}\times b$.
So, the new price is $\dfrac{118}{100}\times x=1.18x$.
Now, we need to find the ratio at which this new price can be reduced to the initial price.
Let us assume that ratio is ‘z’.
So, we gate $1.18x\times z=x$.
$\Rightarrow z=\dfrac{x}{1.18x}$.
$\Rightarrow z=\dfrac{100}{118}$.
$\Rightarrow z=\dfrac{50}{59}$. But this is the ratio of the original and increased price. We need to know what is the ratio that the new price had to decrease.
Now, we subtract this ratio from 1.
So, the decreased ratio = $1-\dfrac{50}{57}=\dfrac{7}{57}$.
So, we have found the ratio at which the price should be decreased such that the price drops down to the initial price as $\dfrac{7}{57}$.

Note: We should not stop after finding the ratio $\dfrac{50}{57}$ as it is not the required answer. We can also find the percentage at which the new price has to be reduced in order to get to the original price by multiplying $\dfrac{7}{57}$ with 100. We should note that it has to be reduced by 18%, as we can see that more amount will be reduced from the new price which is not equal to original price. Similarly, we can expect problems to find the profit percentage, if the shop sells at 30% more than the initial price, whereas he bought at the increased price.