Question

The ratio of number of boys to the number of girls in a school of 1440 students is 7:5. If 40 new boys are admitted, find how many new girls may be admitted to make this ratio 4:3.

Answer 1

Hint:
Here we will first use the given information and find the number of boys and the number of girls in the school. Then we will assume the number of new girls admitted. We will then form an equation using the given condition of the ratio and after solving the equation we will find the number of new girls admitted.

Complete Step by step Solution:
It is given that the ratio of number of boys to the number of girls in a school of 1440 students is 7:5.
Let the number of boys be \[7x\] and the number of girls be \[5x\].
As the total number of students is 1440. Therefore, we get
\[ 7x + 5x = 1440\]
Now by solving this we will get the value of \[x\].
Adding the like terms, we get
\[ \Rightarrow 12x = 1440\]
\[ \Rightarrow x = \dfrac{{1440}}{{12}} = 120\]
Now by using the value of \[x\], we will get the number of boys and the girls in the school. Therefore, we get
Number of boys \[ = 7 \times 120 = 840\]
Number of girls \[ = 5 \times 120 = 600\]
It is given that if 40 new boys are admitted and let \[y\] be the number of girls admitted then the ratio will become 4:3. So we will form the equation of this condition to get the value of the number of girls admitted. Therefore, we get
\[ \dfrac{{840 + 40}}{{600 + y}} = \dfrac{4}{3}\]
Now we will solve this to get the value of \[y\]. Therefore, we get
\[ \Rightarrow 880 \times 3 = 4\left( {600 + y} \right)\]
Multiplying the terms, we get
\[ \Rightarrow 2640 = 2400 + 4y\]
Subtracting the like terms, we get
\[ \Rightarrow 4y = 2640 - 2400 = 240\]
Dividing both side by 4, we get
\[ \Rightarrow y = \dfrac{{240}}{4} = 60\]

Hence the number of new girls may be admitted to make this ratio \[4:3\] is 60.

Note:
Here, we have given the number of boys and girls given a ratio. The ratio is the form in which the data is written in the compact form by simply canceling out the common factors from the numbers. The ratio is generally used to represent the large number data. We have used the ratio and given information to form a linear equation. A linear equation is an equation in which the highest degree is 1 and has only one solution.