Question

The ratio between the number of boys and girls in a school is $4:5$. If the number of boys is increased by $30\% $ and the number of girls by $40\% $, then what will be the new ratio of boys and girls in the school?

Answer 1

Hint: Here we will use the concepts of the percentage which is expressed as the fraction where the numerator is expressed upon the numerator. Here we will assume the unknown given ratio with respect to the some common factor “x”.

Complete step by step answer:
Let us assume that the number of boys and the girls in the school are $4x$ and $5x$ respectively.
Also given that, increased number of boys is $30\% $ and the increased number of girls is $40\% $
Hence, the increased number of boys can be represented as: $130\% $ of \[4x\]
It can be mathematically expressed as- (Percentage is always expressed as the numerator upon the hundred)
Increased number of boys $ = \dfrac{{130}}{{100}} \times 4x$ ….. (A)
Similarly, the increased number of girls is given $140\% $ of \[5x\]
It can be mathematically expressed as-
Increased number of girls $ = \dfrac{{140}}{{100}} \times 5x$ ….. (B)
By using the equations (A) and (B)
The new ratio of boys and girls is given by $ = \dfrac{{\dfrac{{130}}{{100}} \times 4x}}{{\dfrac{{140}}{{100}} \times 5x}}$
Common factors from the numerator and the denominator cancel each other.
The new ratio of boys and girls is given by $ = \dfrac{{13 \times 4}}{{14 \times 5}}$
Find factors for the above expression –
The new ratio of boys and girls is given by $ = \dfrac{{13 \times 2 \times 2}}{{2 \times 7 \times 5}}$
Common factors from the numerator and the denominator and therefore remove from the numerator and the denominator.
The new ratio of boys and girls is given by $ = \dfrac{{26}}{{35}}$
Therefore, the new ratio of boys and the girls is given by $26:35$

Note:
Always remember that the ratio is the comparison between the two similar terms or the objects and is unitless. Ratio can be converted to its equivalent fraction by multiplying and dividing the same number. Be good in multiples and division and the simplification of the fraction by using factorization.