There were 120 fewer boys than girls in a school hall. After 20% of the girls left the hall and 70% more boys entered the hall,there were 321 children in the hall.how many girls remain in the hall?
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Question
Answer
20% = 20/100 = 1/5
This means 1/5 of the girls left the hall.
70% = 70/100 = 7/10
This means that there were originally 10 units of boys and an additional 7 units of boys entered the hall.
At first:
Boys → 10 units
Girls → 10 units + 120
After 1/5 of the girls left the hall, the number of girls remaining is:
4/5 × (10 units + 120) = 8 units + 96
After 70% more boys entered the hall, the number of boys became:
10 units + 7 units = 17 units
Since there were 321 children in the hall in the end,
8 units + 96 + 17 units = 321
25 units + 96 = 321
25 units = 321 – 96
= 225
1 unit = 225 ÷ 25
= 9
8 units = 9 × 8
= 72
72 + 96 = 168 girls remaining