question_answer 1)

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. TIPS Firstly, find the number of boys, which is obtained on subtracting the number of girls from total number of students and then find the required ratios

Answer:

                Given, number of girls = 2300 and total number of students = 4320 \[\therefore \]Number of boys = Total number of students - Number of girls = 4320 ? 2300 = 2020 (a) Required ratio \[\text{=}\frac{\text{Number}\,\text{of}\,\text{girls}}{\text{Total}\,\text{number}\,\text{of}\,\text{students}}\text{=}\frac{\text{2300}}{\text{4320}}\] \[\because \]\[2300=2\times 2\times 5\times 5\times 23\]and \[4320=2\times 2\times 5\times 2\times 2\times 2\times 3\times 3\times 3\] \[\therefore \] HCF of 2300 and \[4320=2\times 2\times 5=20\] \[\frac{2300\div 20}{4320\div 20}=\frac{115}{216}=115:216\] (b) Required ratio \[\text{=}\frac{\text{Number}\,\text{of}\,\text{boys}}{\text{Number}\,\text{of}\,\text{girls}}=\frac{2020}{2300}\] \[\because \]\[2020=2\times 2\times 5\times 101\]and \[2300=2\times 2\times 5\times 5\times 23\] \[\therefore \] HCF of 2020 and \[2300=2\times 2\times 5=20\] \[=\frac{2020\div 20}{2300\div 20}=\frac{101}{115}=101:115\] (c) Required ratio \[\text{=}\frac{\text{Number}\,\text{of}\,\text{boys}}{\text{Total}\,\text{number}\,\text{of}\,\text{students}}=\frac{2020}{4320}\] \[\because \]\[2020=2\times 2\times 5\times 101\]and \[4320=2\times 2\times 5\times 2\times 2\times 2\times 3\times 3\times 3\] \[\therefore \]HCF of 2020 and \[4320=2\times 2\times 5=20\] \[=\frac{2020\div 20}{4320\div 20}=\frac{101}{216}=101:216\]