Read the following and answer the questions that follow.
The Govind Public school with classes 9 to 12 has a total of 1230 students, consisting of both girls and boys. In Class 11, the ratio of girls to boys is 6 : 7, with the number of boys exceeding girls by 30. In Class 9, the number of boys is 20 more than that in Class 10. The number of girls in Class 10 is 25 more than that in Class 9. The number of girls in Class 11 is 5 more than the number of boys in Class 12. The combined strength of Classes 9 and 10 compared to the combined strength of Classes 11 and 12 is in the ratio 103 : 143. Additionally, the ratio of boys to girls in Class 10 is 5 : 8.
Find the ratio of the total number of boys to that of girls in the Govind Public school.
Solution
For class 11th, let us assume that the number of boys and girls are 7x and 6x respectively.
We are given that 7x - 6x = 30 ==> x = 30.
Boys in 11th = 210
Girls in 11th = 180.
The combined strength of Classes 9 and 10 compared to the combined strength of Classes 11 and 12 is in the ratio 103 : 143 and total strength of the school is 1230.
Combined strength of 11th and 12th = 715.
Combined strength of 9th and 10th = 515.
The number of girls in Class 11 is 5 more than the number of boys in Class 12.
Boys in 12th = 175.
Girls in 12th = 715 - (175) - (210 + 180) = 150.
the ratio of boys to girls in Class 10 is 5 : 8. Let us assume the number of boys and girls to be 5y and 8y respectively.
In Class 9, the number of boys is 20 more than that in Class 10. The number of girls in Class 10 is 25 more than that in Class 9.
Boys in 9th = 5y + 20.
Girls in 9th = 8y - 25.
Total students in 9th and 10th ==> 13y + 13y - 5 = 515
==> y = 20.
Boys in 9th = 120.
Girls in 9th = 135.
Boys in 10th = 100.
Girls in 10th = 160.
Boys in 11th = 210
Girls in 11th = 180.
Boys in 12th = 175.
Girls in 12th = 150.
the ratio of the total number of boys to that of girls in the Govind Public school = 120+100+210+175 : 135+160+180+150 = 605:625 = 121 : 125.
