Problem Solving

swerve wrote:From a group of boys and girls, 15 girls leave. There are then left two boys for each girl. After this 45 boys leave. There are then 5 girls for each boy. The number of girls in the beginning was?

A. 29
B. 40
C. 43
D. 48
E. None of these

The OA is B.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.

Say there were x girls.

After the 15 gilrs left, the number of girls left = (x - 15)
=> the number of boys now = 2(x - 15) = 2x - 30; it is given that there are then left two boys for each girl

After 45 boys left, the number of boys left = 2x - 30 - 45 = 2x - 75
=> the number of girls now = 5(2x - 75) = 10x - 375; it is given that there are then 5 girls for each boy

10x - 375 must be equal to x - 15

Thus, 10x - 375 = x - 15

=> x = 40

The correct answer: B

Hope this helps!

-Jay
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swerve wrote:From a group of boys and girls, 15 girls leave. There are then let two boys for each girl. After this 45 boys leave. There are then 5 girls for each boy. The number of girls in the beginning was?

A. 29
B. 40
C. 43
D. 48
E. None of these

We can let b = number of boys and g = number of girls originally in the group. Thus, we have:

b/(g - 15) = 2/1

and

(b - 45)/(g - 15) = 1/5

Simplifying the first equation, we have:

b = 2(g - 15)

b = 2g - 30

Substituting this into the second equation, we have:

(2g - 30 - 45)/(g - 15) = 1/5

5(2g - 75) = g - 15

10g - 375 = g - 15

9g = 360

g = 40

Answer: B