SOLUTION: An amount of money was divided between some people in such a way that if there had been 4 more people,everyone would have got Tk.16 less. But if there had been 4 less people, every

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Question 1002035: An amount of money was divided between some people in such a way that if there had been 4 more people,everyone would have got Tk.16 less. But if there had been 4 less people, everyone would have got Tk.24 more. How many people were in group.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
An amount of money was divided between some people in such a way that if there had been 4 more people,everyone would have got Tk.16 less.
But if there had been 4 less people, everyone would have got Tk.24 more. How many people were in group.
:
let a = total amt to be divided
let n = no. of people in the group
:
write an equation for each scenario, simplify as much as possible
a%2Fn - a%2F%28%28n%2B4%29%29 = 16
multiply eq by n(n+4)
a(n+4) - an = 16n(n+4)
an + 4a - an = 16n^2 + 64n
4a = 16n^2 + 64n
simplify, divide by 4
a = 4n^2 + 16n
and
a%2F%28%28n-4%29%29 - a%2Fn = 24
an - a(n-4) = 24n(n-4)
an - an + 4a = 24n^2 - 96n
4a = 24n^2 - 96n
a = 6n^2 - 24n
a=a, therefore
6n^2 - 24n = 4n^2 + 16n
6n^2 - 4n^2 - 24n - 16n = 0
2n^2 - 40n = 0
factor out 2n
2n(n - 20) = 0
n = 20 people in the group
:
:
To check this out, find the total of amt to be divided (a)
a = 4n^2 + 16n
replace n with 20
a = 4(400) + 16(20)
a = $1920
See if this works out
1920%2F20 - 1920%2F24 =
96 - 80 = $16 less
You can check this out in the other scenario, $24 more with 16 people