P6 Math: Teachers and Pupils

20% of the people in a school hall are teachers and the rest are pupils. 75% of the pupils are boys and there are 72 more boys than girls. How many boys must leave the hall so that 20% of the people in the hall are boys ?

Here is another ratio problem, similar to previous post of red and white roses.

Ratio of each group:

Teachers: 20% of people

Boys: 75% of 80% of people = 3/4 * 4/5 = 60% of people

Girls: 80% - 60% = 20% of people

T : B : G = 20 : 60 : 20

Since only boys must leave the hall, the number of teachers and girls are unchanged.

At first :       T : B : G  = 2u : 6u : 2u --> B : (T + G) = 6u : 4u

At the end (boys left only 20% ):            B : (T + G) = 2u : 8u = 1u : 4u

From first ratio, boys are more than girls by (6u - 2u) = 4u --> 4u = 72 or u = 18.

Number of boys reduced from 6u to 1u --> 5u.

This is the number of boys that must  leave the hall 5u --> 5 * 18 = 90 boys.