# Question

There were 870 children in a stadium at first. After, 2/5 of the girls and 1/3 of the boys went home 1.5 hours later, there were still 48 more boys than girls in the stadium. How many children went home 1.5 hours later ?

I worked out the following.  Not sure whether it is correct. Looking for some easy solutions.

2/3 boys = 3/5 girls + 48 —– (1)

1/3 boys = 3/10 girls + 24  —– (2) — divided by 2

Boys = 9/10 girls + 24

Girls = 10u

Total 870 = 10u + (9u+72) = 19u+72

1u = 870+72  / 19 = 42

Therefore, Girls = 420  Boys = 450

Those who left = 150 + 84 = 234 children

Method 1 :
Before —
girls : 5u
boys : 3p
After —
girls : 5u – 2u = 3u
boys : 3p – 1p = 2p
5u + 3p ——- 870
10u + 6p ——- 1740
2p – 3u ——- 48
6p – 9u ——- 144
10u + 9u = 19u ——- 1740 – 144 = 1596
1u ——- 84
2p – 3 x 84 = 2p – 252 ——- 48
1p ——- (48 + 252)/2 = 150
2 x 84 + 150 = 318

Method 2 :
5/5 girls + 3/3 boys ——- 870
10/5 +6/3 boys ——- 1740
2/3 boys – 3/5 girls ——- 48
6/3 boys – 9/5 girls ——- 144
10/5 + 9/5 = 19/5 ——- 1740 – 144 = 1596
5/5 girls ——- (1596/19) x 5 = 420
(2/5) x 420 = 168
870 – 420 = 450
450/3 = 150
150 + 168 = 318

Ans : 318 children.

Thank you so much for the answer and for your time. Appreciate very much.

You are most welcome.

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3 units boys + 5 units girls –> 870

6 units boys + 10 units girls –>1740

2 units boys – 3 units girls –> 48

6 units boys – 9 units girls –> 144

19 units of girls –> 1740 -144

= 1596

1 unit of girls –> 1596÷19

= 84

3 units of girls –> 3 × 84

= 252

2 units of boys –> 252 + 48

= 300

1 unit of boys –> 150

Total went

home –>2 units of girls + 1 unit of boys

= 2×84 + 150

= 318 (Ans)

Thank you very much for the answer and explanation.  Appreciate very much.

Hi VSK,

You may wish to note the following:

2/3 boys = 3/5 girls + 48 —– (1)

1/3 boys = 3/10 girls + 24  —– (2) — divided by 2

Boys = 9/10 girls + 72

Girls = 10u

Total 870 = 10u + (9u+72) = 19u+72

1u = 87072  / 19 = 42

Therefore, Girls = 420  Boys = 450

Those who left = 150 + 168 = 318 children

(Because 2/5 of girls and 1/3 of boys went home)

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