Catholic High Sch 2006 PSLE Math Prelim Q47

Camp A and Camp B had a total of 350 children. Camp A was for girls whereas Camp B was for boys. There were 2/5 as many girls as boys. Midway, more pupils joined both camps and for every 2 additional girls who joined Camp A, 1 additional boy joined Camp B. Given that there is an equal number of boys and girls in the end, how many boys joined Camp B midway?

Solution

At first -----
Girls ----- 2 units
Boys ----- 5 units
Boys more than girls ----- 5 units – 2 units = 3 units

(Total boys and girls) 7 units ----- 350
1 unit ----- 350 divided by 7 = 50

Girls ----- 2 units x 50 = 100
Boys ----- 5 units x 50 = 250
Boys more than girls ----- 250 – 100 = 150

From the above, we conclude that (boys more than girls)
3 units ---- 150

To have equal number of boys and girls in the end, an additional 3 units of boys and 6 units of girls must join, so that both girls and boys will have 8 units each.

(Note that for every 1 additional boy who joined Camp B, 2 additional girls joined Camp A, hence, ratio is 1:2. Likewise, 3 units of boys and 6 units of girls correspond to the ratio 1:2)

Therefore, 3 units of boys joined Camp B midway -----
3 units ----- 150

Answer: 150 boys joined Camp B.