In a college out of 4300 , students 2300 girls find the ratio of a) number of girls to the total number of students b) number of boys to the number of girls
Answers
Answer:
101:216
Step-by-step explanation:
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.