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In a college, out of 4320 students, 2300 are girls. Find the ratio of
(a) Number of girls to the total number of students.
(b) Number of boys to the number of girls.
(c) Number of boys to the total number of students.

Solution:

Total number of students = 4320

Number of girls = 2300

Number of boys = Number of students - Number of girls

= 4320 – 2300

= 2020

(a) Ratio of number of girls to the total number of students = Number of girls / Total number of students

= 2300 / 4320

The factors of 2300 are 2 × 2 × 5 × 5 × 23 and the factors of 4320 are 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 5

Now, the HCF of 2300 and 4320 is 2 × 2 × 5 = 20.

= (2 × 2 × 5 × 115) / (2 × 2 × 5 × 216)

= 115 / 216

Therefore, 115 : 216 is the ratio of the number of girls to the total number of students.

(b) Ratio of number of boys to the number of girls

= Number of boys / Number of girls

= 2020 / 2300

= (2 × 2 × 5 × 101) / (2 × 2 × 5 × 115)

= 101 / 115

Therefore, the ratio of the number of boys to the number of girls is 101 : 115.

(c) Ratio of number of boys to the total number of students

= Number of boys / Total number of students

= 2020 / 4320

= (2 × 2 × 5 × 101) / (2 × 2 × 5 × 216)

= 101 / 216

Therefore, 101 : 216 is the ratio of the number of boys to the total number of students.

NCERT Solutions for Class 6 Maths Chapter 12 Exercise 12.1 Question 10

In a college, out of 4320 students, 2300 are girls. Find the ratio of (a) Number of girls to the total number of students. (b) Number of boys to the number of girls. (c) Number of boys to the total number of students.

Summary:

It is given that in a college, out of 4320 students, 2300 are girls. We have found the ratio of (а) 115:216 is the ratio of number of girls to the total number of students. (b) 101:115 is the ratio of number of boys to the number of girls. (c) 101:216 is the ratio of number of boys to the total number of students.

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