There were 100 children at a festival. after 36 of the boys left the festival and another 21 girls
joined the festival, the ratio of the number of boys to the number of girls became 8 : 9. how many more boys than girls were originally at the festival?

There were 52 more boys than girls originally at the festival.

Let "b" be the number of boys at festival

Let "g" be the number of girls at festival

Given that There were 100 children at a festival

Number of boys + number of girls = 100

b + g = 100 --------- eqn 1

After 36 of the boys left the festival and another 21 girls  joined the festival, the ratio of the number of boys to the number of girls became 8 : 9

36 of the boys left the festival means: b - 36

Another 21 girls  joined the festival means: g + 21

Now the ratio is 8 : 9

On cross multiplication we get,

9b - 324 = 8g + 168

9b - 8g = 492 ----------- eqn 2

Let us solve eqn 1 and eqn 2 to find values of "b" and "g"

From eqn 1 we get,

b = 100 - g ---- eqn 3

Substitute eqn 3 in eqn 2,

9(100 - g) - 8g = 492

900 - 9g - 8g = 492

900 - 17g = 492

17g = 408

g = 24

Therefore from eqn 3,

b = 100 - g = 100 - 24 = 76

b = 76

Thus, number of boys originally at the festival = 76

number of girls originally at the festival = 24

This means we have to find out difference between number of boys and number of girls

Number of boys more than girls = number of boys - number of girls

Number of boys more than girls = 76 - 24 = 52

Thus there were 52 more boys than girls originally at the festival.

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