Question

The price of a dress was Rs.500. In December 2006 the price was increased by 10%. During October 2007 it was reduced by 10%. What is the new price of the shirt?

Answer 1

Hint: In this question, using the percent formula which is given by \[\dfrac{x}{100}\times y\] we need to find 10% of 500 and add that to 500. Now, we get the price in 2006 then again find 10% of that price and subtract it from the price in 2006 using the percent formula to get the new price in 2007. Now, on further simplification we get the result.

Complete step by step solution:
Now, as we already know that x percent of y is given by the formula
\[\dfrac{x}{100}\times y\]
Let us now find the 10% of Rs.500 using the above percent formula
Now, on comparison we get,
\[x=10,y=500\]
Now, on substituting the respective values in the formula we get,
\[\Rightarrow \dfrac{10}{100}\times 500\]
Now, on simplifying this further we get,
\[\Rightarrow 50\]
Let us now find the price in 2006 after increasing 10%
\[\Rightarrow 500+50\]
Now, on further simplification we get,
\[\Rightarrow 550\]
Thus, the price of the shirt in 2006 is Rs.550
Now, let us find the price of the shirt in 2007
As already given in the question that it decreases by 10% in 2007 we get,
Now, we need to calculate the value of 10% in Rs.550
Now, on comparing with the above percent formula we get,
\[x=10,y=550\]
Now, on substituting respective values in the formula we get,
\[\Rightarrow \dfrac{10}{100}\times 550\]
Now, on further simplification we get,
\[\Rightarrow 55\]
Now, the price of the shirt in 2007 can be calculated by
\[\Rightarrow 550-55\]
Now, on simplifying this further we get,
\[\Rightarrow 495\]
Hence, the new price of the shirt is Rs.495

Note:
Instead of finding the percentage value separately and then adding or subtracting we can directly find it using the formula for profit and loss and then calculate which gives the result directly. This method has fewer steps.
It is important to note that we need to add the percentage value to the given price when it increases and then subtract the percentage value when it decreases. It is also to be noted that to find the new value of a shirt we need to calculate it with respect to the price in 2006 because it will be the price before decreasing but not Rs.500.