100 people go to a party there are 100 plates of food each male eats in 4 plates, each female eats in 3 plates and 4 children eat in one plate and all the plates are used. what is the total no of each male female and chlidren?
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It can be done only by hit and trial method as there are only two equation and 3 unknown .
But if you are applying some logic in it then you will get the solution very fast as many case will eliminate .
Solution is : No. of children = 76 , No of Women = 15 and No. of men = 9
First find the number of children . It can only be multiple of 4 and can only be 76 as if its less than 76 say 72 then if all other are women then number of plate will be 72/4 + 28*3 = 18+84 = 102 which is greater than 100 . Similarly you can discard all the other No. of children less than 76.
If you are taking No. of children = 76 then total plate used will be 19 and left plates are 81 .
Also number of person remaining is 24(100-76=24)
Let x number of person be women , then no. of men = (24-x)
x*3 + (24-x)*4=81
or, x = 15
No . of children = 76
No. of Women = 15
No of Men = 100- (76+15) = 100-091 = 9
Hope this would have cleared your doubt .
But if you are applying some logic in it then you will get the solution very fast as many case will eliminate .
Solution is : No. of children = 76 , No of Women = 15 and No. of men = 9
First find the number of children . It can only be multiple of 4 and can only be 76 as if its less than 76 say 72 then if all other are women then number of plate will be 72/4 + 28*3 = 18+84 = 102 which is greater than 100 . Similarly you can discard all the other No. of children less than 76.
If you are taking No. of children = 76 then total plate used will be 19 and left plates are 81 .
Also number of person remaining is 24(100-76=24)
Let x number of person be women , then no. of men = (24-x)
x*3 + (24-x)*4=81
or, x = 15
No . of children = 76
No. of Women = 15
No of Men = 100- (76+15) = 100-091 = 9
Hope this would have cleared your doubt .
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