The ratio of boys and girls in the class is 4:3. If 5 more boys join the class and 3 girls leave the class, then the ratio of boys and girls becomes 11:6. What is the number of girls in the class now?
- A18
- B24
- C27
- D21
Solution & Step-by-step Explanation
Let the initial number of boys and girls be 4x and 3x respectively.
According to the changes:
New number of boys = 4x+5
New number of girls = 3x−3
The new ratio becomes 11:6:
3x−3
4x+5
=
6
11
Cross-multiplying to solve for x:
6(4x+5)=11(3x−3)
24x+30=33x−33
33x−24x=30+33
9x=63⟹x=7
Initial number of girls = 3x=3×7=21
New number of girls in the class now = 3x−3=21−3=18
According to the changes:
New number of boys = 4x+5
New number of girls = 3x−3
The new ratio becomes 11:6:
3x−3
4x+5
=
6
11
Cross-multiplying to solve for x:
6(4x+5)=11(3x−3)
24x+30=33x−33
33x−24x=30+33
9x=63⟹x=7
Initial number of girls = 3x=3×7=21
New number of girls in the class now = 3x−3=21−3=18