Question : The ratio of the number of boys to girls in a village is 3 : 2. If 30% of boys and 70% of girls appeared in an examination, the ratio of the number of villagers who appeared in the examination to that not appeared in the same examination is:
Option 1: 9 : 14
Option 2: 23 : 27
Option 3: 1 : 1
Option 4: 27 : 23
Correct Answer: 23 : 27
Solution : The ratio of the number of boys to that of girls in a village = 3 : 2 Let the number of boys be $3x$ and number of girls be $2x$. Number of boys appeared in the examination = $3x × 0.3 = 0.9x$ Number of girls appeared in the examination = $2x × 0.7 = 1.4x$ Ratio of numbers of villagers appeared : Ratio of villagers not appeared = (0.9 + 1.4) : (5 – (0.9 + 1.4)) = 2.3 : 2.7 = 23 : 27 Hence, the correct answer is 23 : 27.
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Question : Directions: One day, 90 students were traveling in a bus and the ratio of the number of boys to girls was 2: 1. The next day, the number of students remained the same, but the ratio of the number of boys to girls became 3: 2. What was the difference between the numbers of boys traveling in the bus on both the days?
Option 1: 18
Option 2: 6
Option 3: 14
Option 4: 30
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 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 : The ratio of the radii of two cylinders is $2:3$ and the ratio of their heights is $5:3$. The ratio of their volumes will be:
Option 1: $9:4$
Option 2: $20:27$
Option 3: $4:9$
Option 4: $27:20$
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
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