Question

A school has 630 students. The ratio of the number of boys to the number of girls is $3:2$ . The ratio changes to $7:5$ after the admission of 90 new students. Find the number of newly admitted boys.

Answer 1

Hint: Here we will use the simple concepts of linear equations i.e, the total number of students will be equal to the sum of the ratio of boys and girls.Consider 3x be the number of boys and 2x be the number of girls then total number of students is calculated by sum of number of boys and girls and equating to 630 and compute x and y values.Similarly calculate for the new ratio formed when new students got admitted, then total number of boys and girls sum will be 720 and find the values of x and y,the difference of x values from both ratio gives newly admitted boys.

Complete step-by-step answer:
 We have given the ratio of the number of boys to the number of girls is $3:2$.
 So, let the number of boys be $3x$ and the number of girls be$2x$. According to the question total number of students are $630$
$\therefore 3x + 2x = 630 \Rightarrow 5x = 630 \Rightarrow x = 126$ .
Hence, the total number of boys are $3x = 3 \times 126 = 378$ and
The total number of girls are $2x = 2 \times 126 = 252$ .
After admission of 90 new students, the total number of students $ = 630 + 90 = 720$ and the ratio shifted to $7:5$ . Let the number of boys and girls be $7x{\text{ and }}5x$ respectively.
 Therefore,
$7x + 5x = 720 \Rightarrow 12x = 720 \Rightarrow x = 60$ .
Then the total number of boys are$7x = 7 \times 60 = 420$ and
The total number of girls are $5x = 5 \times 60 = 300$ .
Therefore, the newly admitted boys will be $ = 420 - 378 = 42$ boys.

Note: Here we use the information, $a:b$ is the actual ratio then $a + b$ will give us the total count. The number of newly admitted boys is calculated by subtracting the total number of boys when the students are 630 from the total number of boys when students are 720.