Latest Others Aptitude Question SOLUTION: At a local village gala, the entire population turned up, 500 people. The event raised £3,000. Tickets were priced as follows: £7.48 men £7.12 women £0.45 children. How many me

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(#M40009066) OTHERS question men,women and children Keep an EYE

At a local village gala, the entire population turned up, 500 people. The event raised £3,000. Tickets were priced as follows:
£7.48 men
£7.12 women
£0.45 children.
How many men,women and children were there?

Asked In Others Raman (12 years ago)

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Bankim  (12 years ago)

m + w + c = 500
m = 500 - w - c
748m + 712w + 45c = 300 000

Now

748 (500 - w - c) + 712w + 45c = 300 000
374 000 - 748w - 748c + 712w + 45c = 300 000
74 000 = 36w + 703c

solving this for integer values of m,w,c
we get

m= 149, w = 259, c= 92

Is this solution Helpfull? Yes (4) | No (1)  

Vignesh  (12 years ago)

Women = 259
Men = 149
Children = 92

Women = 259 *7.12 = 1844.08
Men = 149 *7.48 = 1114.52
Children = 92 *0.45 = 41.4

Total :
Men + Women + Children = 149 + 259 + 92 = 500 peoples.
1844.08 + 1114.52 + 41.4 = 3000

Is this solution Helpfull? Yes (3) | No (3)  

Vignesh  (12 years ago)

Women = 259
Men = 149
Children = 92

Women = 259 *$7.12 = $1844.08
Men = 149 *$7.48 = $1114.52
Children = 92 *$0.45 = $41.4

Total :
Men + Women + Children = 149 + 259 + 92 = 500 peoples.
$1844.08 + $1114.52 + $41.4 = $3000

Is this solution Helpfull? Yes (2) | No (3)  

Leena  (12 years ago)

@ Vignesh,

How did you get these values ?

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Le Noir Yanncik  (3 years ago)

w is women
c is children
(500-w-c) 7.48 + 7.12 w + 0.45 c = 3000
so we get 0.36w + 7.03 c = 740
multipy by 100
36w + 703 c = 74000
Then : if men were the only one it will make 500 x 7.48 = 3740 so 740 too much
if women were the only one it will make 500 x 7.12 = 3560 so 560 too much
So, we may considere that the maximum children is 740/7.48-0.45 = 105
And the less children possible is 560/7.12-045 = 84
Let take the median between 105 and 84 = 95
Now check around 95 children to find the only integer possible :
Nb of women for 95 children = (74000-703 x 95) / 36 = 200,4167 women not OK
Nb of women for 94 children = (74000-703 x 94) / 36 = 219,9444 women not OK
Nb of women for 96 children = (74000-703 x 96) / 36 = 180,8889 women not OK
Nb of women for 93 children = (74000-703 x 93) / 36 = 239,4720 women not OK
Nb of women for 97 children = (74000-703 x 97) / 36 = 161,3611 women not OK
Nb of women for 92 children = (74000-703 x 92) / 36 = 259 women THIS IS OK
Why divide by 36 ? because each time we increase the nb of women the total is +36
So, in a very few operations we find 92 children, 259 women and 500-259-92 = 149 men

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