The ratio of girls in a school is 5:2. The number of boys is more by 450 than that of girls. How many students are there in that school? A) 650 B) 1050 C) 400 D) 950
Hint: In this question we don’t have the exact number in spite of ratios of the number of girls and number of boys. Consider the total number of the students in the school as x and then proceed with the solution.
Complete step-by-step answer: Total no. of the student in the school = x Number of girls = \[2x\] Number of boys = $5x$ We have the ratio of number of girls and number of boys Boys : Girls= \[5x:2x\] As given in the question, the number of boys is more by 450 than that of girls. So, our equation is $5x - 2x$ which is equal to $450$ $5x - 2x = 450$ After subtracting $3x = 450$ $x = 450/3$ Dividing the 450 by 3 $x = 150$ From here we find out the value of $x$ which is $150$. We have the ratio of numbers of boys and girls. So, we add the ratio to find out the total number of students. $ = 5x + 2x$ $ = 7x$ Now we know the value of x so, put his value in this $ = 7.150$ Here we multiply 7 by 150 $ = 1050$ The option B is the correct option in all, total number of students are $1050$.
Note: 5:2 ratio does not mean 5 boys and 2 girls. 5:2 ratio is equal to 5x boys and 2x girls where x is any natural number. Here we have the numbers of girls and the numbers of boys in the ratio.