Question : In a college union, there are 48 students. The ratio of the number of boys to the number of girls is 5 : 3. What is the number of girls to be added to the union so that the ratio of boys to girls is 6 : 5?
Option 1: 6
Option 2: 7
Option 3: 12
Option 4: 17
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Correct Answer: 7
Solution : Given: Total number of students = 48 The ratio of the number of boys to the number of girls = 5 : 3 Number of boys = $\frac{5}{8}×48=30$ Number of girls = $\frac{3}{8}×48=18$ Let the $x$ number of girls to be added. Then, according to the given conditions: $\frac{30}{(18+x)}=\frac{6}{5}$ ⇒ $30×5=6×(18+x)$ ⇒ $150=108+6x$ ⇒ $6x=42$ $\therefore x=7$ Hence, the correct answer is 7.
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Question : The ratio of the number of boys to the number of girls in a school of 432 pupils is 5 : 4. When some new boys and girls are admitted, the number of boys increases by 12 and the ratio of boys to girls changes to 7 : 6. The number of new girls admitted is:
Option 1: 12
Option 2: 14
Option 3: 24
Option 4: 20
Question : In a school, there were 1554 students, and the ratio of boys to girls was 4 : 3. After a few days, 30 girls joined the school but a few boys left. As a result, the ratio of boys and girls became 7 : 6. The number of boys who left the school is:
Option 1: 76
Option 2: 74
Option 3: 84
Option 4: 86
Question : The ratio of the number of boys in a school to the total number of boys and girls in that school is 7 : 17. If the number of boys in that school is 1099, then how many girls are there in that school?
Option 1: 1570
Option 2: 1580
Option 3: 1560
Option 4: 1550
Question : The arithmetic mean of the following numbers 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7 is:
Option 1: 4
Option 2: 5
Option 3: 14
Question : The ratio of the present ages of the two boys is $3:4$. After 3 years, the ratio of their ages will be $4:5$. The ratio of their ages after 21 years will be:
Option 1: $14:17$
Option 2: $17:19$
Option 3: $11:12$
Option 4: $10:11$
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