Solutions to questions on percentages

Have given below solutions to the questions 4 and 5 on percentages .

4. In a class, if 50% of the boys were girls, then there would be 50% more girls than boys. What percentage of the overall class is girls?

For questions of this type, it is best to go from the final step. In the final state, the number of girls should be 1.5 * the number of boys.

When 50% of the boys are taken as girls, let the number of boys = x
Number of girls = 1.5x
total number of students = 2.5x

Original number of boys = 2x (50% of boys = x)
Original number of girls = 0.5x

Girls form 20% of the overall class.

5. Class B has 50% more students than class A. Number of girls in class A is equal to number of boys in class B. The percentage of girls is the same in both classes. What percentage of the student group are boys?

Let number of girls in class A = x
Let number of boys in class A = y
Total number of students = x + y
Proportion of girls = x/(x+y)

Number of boys in class B = x.
Total number of students in class B = 1.5( x + y)
Proportion of girls = 1 - x/1.5(x+y)

Percentage of boys in the overall student community = (x+y)/2.5* (x + y) * 100 = 40%