Percentage · invariant after joining

Question

In a P6 Math Club, 60% of the pupils were boys at first. Later, 12 girls joined the club and the number of boys did not change. After that, boys made up 50% of the pupils. How many pupils were in the club at first?

Practice: 3 similar questions

1. In Siti's robotics group, 60% of the pupils were boys at first. Later, 5 girls joined and the number of boys did not change. After that, boys made up 50% of the pupils. How many pupils were in the group at first?
   Answer

   25 pupils — At first, boys were 60% = 3/5, so the whole group was 5 units: 3 units boys and 2 units girls. After joining, boys were 50%. The number of boys was unchanged, so boys were still 3 units, and girls also became 3 units. The extra 1 unit = 5 pupils, so 5 units at first = 5 × 5 = 25 pupils.

2. In Ali's art class, 40% of the pupils were girls at first. Later, 12 boys joined and the number of girls did not change. After that, girls made up 25% of the class. How many pupils were in the class at first?
   Answer

   20 pupils — At first, girls were 40% = 2/5, so the class was 5 units and girls were 2 units. After joining, girls were 25% = 1/4. To keep girls as 2 units, write 1/4 as 2/8, so the class after joining was 8 units. The extra boys were 8 − 5 = 3 units. 3 units = 12 pupils, so 1 unit = 4 pupils. At first, the class had 5 units = 5 × 4 = 20 pupils.

3. In Raju's sports enrichment class, 60% of the pupils were boys at first. Later, 20 girls joined and the number of boys did not change. After that, boys made up 40% of the class. How many pupils were in the class at first?
   Answer

   40 pupils — At first, boys were 60% = 3/5. Scale it to 6/10, so the class at first was 10 units and boys were 6 units. After joining, boys were 40% = 2/5. Scale it to 6/15, so the class after joining was 15 units and boys were still 6 units. The extra girls were 15 − 10 = 5 units. 5 units = 20 pupils, so 1 unit = 4 pupils. At first, the class had 10 units = 10 × 4 = 40 pupils.

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