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Question

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?

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

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