CHIJ St Nicholas Girls' Sch 2009 P6 SA1 Paper 2 Q17

The number of boys to the number of girls in Happy Kindergarten was 3:5. The number of boys to the number of girls in Merry Kindergarten was 4:5. Both kindergartens had the same number of boys. When 10 girls from Happy Kindergarten joined Merry Kinderten, the ratio of the number of boys to the number of girls in Happy Kindergarten became 2:3. Find the total enrolment of the 2 kindergartens.

Solution

Happy
B : G
3 : 5
(multiply both by 4)*
12 : 20
(Total units --> 12 + 20 = 32)

Merry
B : G
4 : 5
(multiply both by 3)*
12 : 15
(Total units --> 12 + 15 = 27)

* Happy (x4) and Merry (x3) to make the number of units for boys in both kindergartens the same, because the number of boys are the same for both kindergartens.


After 10 girls left Happy to join Merry,
Ratio in Happy
B : G
2 : 3
(multiply by 6)**
12 : 18

** (x6) to make units for boys 12 again.

Number of units for girls in Happy before transfer --> 20 units
Number of units for girls in Happy after transfer --> 18

20 units - 18 units --> 10
2 units --> 10
1 unit --> 10 divided by 2 = 5

Total for enrolment for both kindergartens
Happy --> 32 units
Merry --> 27 units
32 units + 27 units --> 59 units
59 units --> 59 x 5 = 295

Answer: 295 children

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