Question

A boat priced at INR 1,70,000 is increased in price by \[20\% \]. What is the new price?
The new price is ________ of the old price. As a decimal, this is _______. The new price is _______.

Answer 1

Hint: Here, we will use fractions, decimals, and percentages to obtain the required answers. We will first find the new price of the boat and then add it to find the new price of boat. Then we will compare the old and new price and fill in the blanks.

Complete step-by-step answer:
It is given that the old price of the boat is INR 1,70,000.
The increase in the price of the boat in percent is \[20\% \].
This means that the increase in the price of the boat is \[20\% \] of the old price of the boat.
Therefore, we get
Increase in price of boat \[ = 20\% {\rm{ of 1,70,000}}\]
Simplifying the expression, we get
\[ \Rightarrow \] Increase in price of boat \[ = \dfrac{{20}}{{100}} \times 1,70,000 = 34,000\]
Therefore, we get the increase in price of the boat as INR 34,000.
Now, we know that the new price of the boat is the sum of the old price of the boat, and the increase in the price of the boat.
Thus, we get
New price of the boat \[ = 1,70,000 + 34,000\]
Adding the terms in the expression, we get
\[ \Rightarrow \] New price of the boat \[ = 2,04,000\]
Therefore, we get the new price of the boat as INR 2,04,000.
Now, we will express the new price of the boat as a percentage of the old price of the boat.
First, we will represent the new price of the boat as a fraction of the old price of the boat.
Therefore, we get the fraction
\[ \Rightarrow \] \[\dfrac{{2,04,000}}{{1,70,000}} = \dfrac{6}{5}\]
A fraction can be converted into a percentage by multiplying the fraction by 100.
Therefore, we can find the new price of the boat as a percentage of the old price of the boat as:
\[ \Rightarrow \] \[\dfrac{6}{5} \times 100 = \dfrac{{600}}{5} = 120\% \]
Thus, the new price of the boat is \[120\% \] of the old price.
Finally, we will express the new price of the boat as a decimal multiple of the old price of the boat.
The new price of the boat as a fraction of the old price of the boat is \[\dfrac{6}{5}\].
We will rewrite \[\dfrac{6}{5}\] as a decimal.
Multiplying the numerator and denominator by 2, we get
\[\begin{array}{l} \Rightarrow \dfrac{6}{5} = \dfrac{6}{5} \times \dfrac{2}{2}\\ \Rightarrow \dfrac{6}{5} = \dfrac{{12}}{{10}}\end{array}\]
Therefore, we get the decimal
\[ \Rightarrow \dfrac{6}{5} = 1.2\]
Thus, the new price of the boat is \[1.2\] times the old price of the boat.
Hence, we get the following statement.
The new price is \[120\% \] of the old price. As a decimal, this is \[1.2\]. The new price is INR 2,04,000.

Note: We used the terms ‘fraction’ and ‘percentage’ to find the solution. A fraction is a number which represents a part of a group. It is written as \[\dfrac{a}{b}\], where \[a\] is called the numerator and \[b\] is called the denominator. The group is divided into \[b\] equal parts. The fraction \[\dfrac{a}{b}\] represents \[a\] parts out of \[b\] equal parts of the group.
A percentage is a number represented as a fraction with 100 as the denominator. It helps in comparing fractions with different denominators. Percent is represented by the symbol \[\% \].