At Orchard Station, the ratio of the no. of boys to the no. of girls on the train was 4:7. At Newton Station,

Question

two-fifth of the boys and some girls alighted from the train. The ratio of the no. of boys to the no. of girls then became 6:5. At Novena Station, 13 boys and 25 girls boarded the train and the no. of boys and girls became equal. How many boys and girls were there in the train after it had left Novena Station?

Answer 1

Just work backwards.

At Novena, you had a ratio of 6 : 5. You can write this as:
B = 6x
G = 5x

But then you add 13 boys and 25 girls. So now you have:
B = 6x + 13
G = 5x + 25

Since you are told the number of boys and girls is equal, you can just equate these two expressions:
6x + 13 = 5x + 25
6x - 5x = 25 - 13
x = 12

Now plug x back into the equations to get the number of boys and girls:
B = 6x + 13 = 6(12) + 13 = 85
G = 5x + 25 = 5(12) + 25 = 85

There were 85 boys and 85 girls when leaving Novena station. It is unnecessary to know the number of boys and girls at Orchard stations or how many left at Newton (though if you want to know, you start with 120 boys, and 210 girls. 48 boys and 150 girls leave the train at Newton leaving 72 and 60. Then at Novena you add the 13 and 25 for your final count.)

85 boys and 85 girls were on the train when it left Novena Station.

Answer 2

Ratio of 6:5 entering Novena Station
+ 13B + 25G
Radio of 1:1 leaving Novena Station

Let r equal a number such that when approaching Novena there were 6r boys and 5r girls.

6r + 13 = boys leaving Novena Station
5r + 25 = girls leaving Novena Station

However

6r + 13:5r + 25 = 1:1, so

6r + 13 = 5r + 25
Subtract 5r + 13 from each side
r = 12

6*12 + 13 = 85

85 boys and 85 girls were in the train after it had left Novena Station

Answer 3

let the no.of boys and girls at Orchard Station be 4x and 7x respectively
At Newton Station 2/5of the boys or (2/5X4x)or 8x/5 boys alighted
So,the number of boys remaining=4x-8x/5=12x/5
And the number of girls remaining=(12x/5)X5/6=2x
At novena station,13 boys and 25 girls boarded the train and their no. became equal
So by the problem,
12x/5 +13=2x+25
=>12x+65=10x+125 (multiplying all the terms by 5)
or 12x-10x=125-65=60
=>x=60/2=30
We have already shown that when the train left novena Station there were 2x girls and equal no of boys in the train,
Therefore,there were 60 boys and 60 girls in the train

Answer 4

25 boys and 25 girls -- all the others got off at Novena Station!

Answer 5

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