Question : In a school of 720 students, the ratio of boys to girls is 3 : 5. Find how many new boys may be allowed to the school if 18 new girls are admitted, so that the ratio of boys to girls changes to 2 : 3.
Option 1: 42
Option 2: 44
Option 3: 50
Option 4: 38
Correct Answer: 42
Solution : In a school of 720 students, the ratio of boys to girls is 3 : 5. ⇒ Number of boys in the school $= 720 × \frac{3}{3+5} =720 × \frac{3}{8}= 270$ ⇒ Number of girls in the school $= 720 × \frac{5}{3+5}=720 × \frac{5}{8}= 450$ Given that the number of new girls admitted to the school is 18. Let $x$ be the number of new boys admitted to the school. According to the question, ⇒ $\frac{(270+x)}{450+18}=\frac{2}{3}$ ⇒ $3(270+x)=468×2$ ⇒ $810+3x=936$ ⇒ $3x=126$ $\therefore x=42$ Hence, the correct answer is 42.
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Question : The ratio of the number of boys to girls in a school is 5 : 2. If 87% of the boys and 80% of the girls passed in the annual exams, then find the percentage of students who failed in the annual exams.
Option 1: 18%
Option 2: 16%
Option 3: 15%
Option 4: 17%
Question : The ratio of the number of boys and girls in a school is 3 : 4 respectively. If the number of boys increases by 10% and the number of girls increases by 15%, what will be the new ratio of the number of boys to the number of girls?
Option 1: $\frac{33}{45}$
Option 2: $\frac{35}{46}$
Option 3: $\frac{33}{46}$
Option 4: $\frac{46}{33}$
Question : Directions: A total of 60 students are traveling in a bus. The ratio of the number of boys to that of girls is 2 : 1. Then, 15 boys get down 5 girls get on the bus at the first stop, 5 boys get in and 10 girls get down from the bus at the second stop. What is the ratio of the number of boys to that of girls in the bus after the second stop?
Option 1: 3 : 2
Option 2: 2 : 1
Option 3: 2 : 3
Option 4: 3 : 1
Question : The ratio of the number of boys and girls in a school is 8 : 12. If 50% of boys and 25% of girls are getting scholarships for their studies, what is the percentage of school students who are not getting any scholarships?
Option 1: 65
Option 2: 66
Option 3: 67
Option 4: 68
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