# Question

There are 600 children in Team A and 30% of them are boys.
There are 400 children in Team B and 60% of them are boys.
After some children are transferred from Team B to Team A, 40% of the children in Team A and 60% of the children in Team B are boys.
How many children are transferred from Team B to Team A?

Before :
Team A :
30% x 600 = 180 (boys)
600 – 180 = 420 (girls)

Team B :
60% x 400 = 240 (boys)
400 – 240 = 160 (girls)

After :
Team A :
boys : 4u
girls : 6u

Team B :
boys : 6p
girls : 4p

4u + 6p ——-> 180 + 240 = 420
2u + 3p ——-> 210
6u + 4p ——-> 420 + 160 = 580
3u + 2p ——-> 290
1u – 1p ——-> 80
10u – 10p ——-> 800 (Team A has 800 more children after the transfer)
(1000 – 800)/2 = 100 (Team B has 100 children after the transfer)
400 – 100 = 300

Ans : 300 children.

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This is an high level thinking question, which can be solved via

Inference Thinking Skills with Stacking Model

Take note that for Team B,  the percentage of boys stays the same throughout the transfer.

Team B

Boys  :    Girls

= 60     :    40 =  3      :     2

This means that for every 3 boys transferred out from B,  2 girls must follow.

In team A,  before transfer

Boys     :       Girls

30        :        70 =  3        :         7

0.3 x 600 = 180  (3 blocks)

There were 180 boys in team A at first.

180 /3 = 60

Each block is 60.

The number of children transferred = 60(2 + 3)

= 300

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This is a tricky one. The key is : The total number of boys before and after the movement is the same.

Total boys = (30% x 600) + (60% x 400) = 420
Total girls = (70% X 600) + (40% x 400) = 580
Total = 1000

After movement, in team A
Boys : Girls
= 4 : 6
= 2 : 3

In team A, there are 5units of children.
In team B, there will be 1000 – 5 units of children.

Team B ratio,
Boys : Girls
= 6 : 4
= 3 : 2
= 3/5(1000 -5u) : 2/5(1000 -5u)

2u of boys in team A + 3/5(1000 – 5u) of boys in team B = 420

2u + 600 – 3u = 420
1u = 180

# of boys in team A after movement = 2u = 360
# of girls in team A after movement = 3u = 540
Total in team A = 900.

# of children transferred from team B to team A = 900 – 600 = 300.

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