Question
In two schools A and B, the total number of students is
in the ratio 3:5. The number of boys in school A is 30% less than the number of boys in school B. The number of girls in school B is 900 more than that in school A. If the average number of students in schools A and B is 3600, find the difference between the number of boys and girls in school A.Solution
ATQ, Total students in schools A and B = 3600 * 2 = 7200 Total students in school A = 7200 * 3/8 = 2700 Total students in school B = 7200 – 2700 = 4500 Let the number of girls in schools A and B be x and (x + 900) respectively. 30% less ⇒ boys in A = 70% of boys in B Let the number of boys in school B be 10y. Then boys in school A = 10y * 70/100 = 7y So, x + 7y = 2700 ---(1) 10y + (x + 900) = 4500 x + 10y = 3600 ---(2) (2) – (1): (x + 10y) – (x + 7y) = 3600 – 2700 3y = 900 y = 300 From (1): x + 7*300 = 2700 x + 2100 = 2700 x = 600 Number of boys in school A = 7 * 300 = 2100 Number of girls in school A = 600 Required difference = 2100 – 600 = 1500
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