P6 Percentage ( Minutes To Score)
3 years 2 months ago #1

Tham Lin Ching

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There were 40% more boys than girls who took part in a drawing competition. After 55 boys and 55 girls joined, there were 30% more boys than girls in the competion.
How many boys and girls were there at first?

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P6 Percentage ( Minutes To Score)
2 years 1 month ago #2

Rex Fernando

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This is bit tricky and must use algebra to solve.
Let us assume B boys and G girls at first.
so, B = 1.4G (40% more)

Then:
(B + 55) = 1.3(G + 55)
B + 55 = 1.3G + 71.5
1.4G + 55 = 1.3G + 71.5 (replacing B with 1.4G)
1.4G - 1.3G = 71.5 - 55 = 16.5
Therefore, 0.1G = 16.5 and G = 165.
B = 1.4 X 165 = 231

Girls at first = 165
Boys at first = 231

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P6 Percentage ( Minutes To Score)
2 years 1 month ago #3

Fibonacci

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Karma: 10

Since 40% more boys than girls,
Ratio of B : G = 7 : 5
When 55 boys and 55 girls joined, difference remained unchanged
Ratio (end) B : G = 13 : 10

Make the difference between the two sets of ratios the same:
at first end
B : G : Difference B : G : Difference
7 : 5 : 2 13 : 10 : 3
21 : 15 : 6 26 : 20 : 6

Can you see that the change in boys is 5 units and the change in girls is also 5 units? Hence,
5units = 55
1unit = 11
Total (at first) = 21units + 15units
= 36units
36units = 396

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The following user(s) said Thank You: Mei Yong Loh