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
Correct Answer: 6
Solution : Given: 90 students were traveling in a bus and the ratio of the number of boys to that of girls was 2: 1 According to the question, 2x + x = 90 3x = 90 x = 90 ÷ 3 x = 30 Therefore, Number of Boys = 60, Number of Girls = 30; The next day, the number of students remained the same, but the ratio of the number of boys to that of girls became 3: 2 3x + 2x = 90 5x = 90 x = 90 ÷ 5 x = 18 Therefore, the Number of Boys = 54, The Number of Girls = 36 So the difference between the numbers of boys traveling in the bus = 60 – 54 = 6
Therefore, the difference between the numbers of boys traveling on the bus on both days is 6. Hence, the second option is correct.
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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 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
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
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 : In a school, $\frac{5}{12}$ of the number of students are girls and the rest are boys. $\frac{4}{7}$ of the number of boys who are below 14 years of age, and $\frac{2}{5}$ of the number of girls who are 14 years or above 14 years of age. If the number of students below 14 years of age is 1120, then the total number of students in the school is:
Option 1: 1820
Option 2: 1290
Option 3: 1900
Option 4: 1920
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