Question

ratio of the number of boys and girls in a school is 11:8. if the difference between the number of boys and girls is of 363 thwn determine the total number of students in the school.
please give a appropriate answer. (hint- the answer is 2299) explain the answer.​

Answer 1

Question :-

The ratio of the number of boys and girls in a school is 11girl. If the difference between the number of boys and girls is 363, then determine the total number of students in the school.

$\large\underline{\sf{Solution-}}$

Given that,

The ratio of the number of boys and girls in a school is 11 : 8.

Let assume that

Number of boys in school = 11x

Number of girls in school = 8x

Now, According to statement

The difference between the number of boys and girls is 363.

$\rm \: 11x - 8x = 363$

$\rm \: 3x = 363$

$\rm \: x = \cancel\dfrac{363}{3} = 121$

$\rm\implies \:x \: = \: 121$

Hence,

Number of boys in school = 11x = 11 × 121 = 1331

Number of girls in school = 8x = 8 × 121 = 968

Thus,

Total number of students in school = 1331 + 968 = 2299

Answer 2

Given : Ratio of the number of boys and girls in a school is 11:8. if the difference between the number of boys and girls is of 363 then determine the total number of students in the school.

Explanation : According to the question, here we are given that the ratio of boys : girls is 11 : 8. The difference between the no. of boys and girls is 363. We need to get the total no. of students

So, here let's assume the constant multiple be α

Ratio = 11 : 8

No. of boys be 11α

Whereas, no. of girls be 8α

Difference between them is 363

Now, let's get the value of α

No. of boys - No. of girls = Difference between boys and girls

• 11α - 8α = 363

Subtracting the smaller one from the greater ratio

• 3α = 363

Cross multiplying we get

• α = 121

Now, as we know that no. of boys will be added to the no. of girls to get the total. So,

• Total number of students = 11α + 8α

Putting α = 121 we get

• Total number of students = 19α

• Total number of students = 19(121) ➝ 2299

Henceforth, the total number of students is 2299