An amount of money was divided between some people in such a way that

Ans : C

Solution - Let the no of people be x and the amount that each one gets be y . Thus the total amount - xy

Given Condition 1 - (x+4)(y-16) = xy (The total amount remains the same because there is a change in the no of people and the amount that each one gets according to the given condition).

SOlving - y-4x=16

GIven condition 2 - (x-4)(y+24) = xy. Solving , -y+6x=24.

Solving both the equations - x=20

@ Brunel - I agree with dave13 .

I too assumed if there had been 4 more people in the first part of the problem.

I dont understand why i always write wrong equations when it comes to such problems. here is what i did, --- logically my approach should be correct ...

Let X be a total sum
N = number of persons
y = sum each owns after division

x / n+4 = y-16 from here follows---> x= n+4y-64

x / n-4= y+24 from here follows ---> x = n-4y-96

after this i simply got stuck what next ?

We can let the number of people = n and the amount of money each originally received = m; thus, the total original amount of money is mn.

If there had been 4 more people, everyone would have $16 less:

(n + 4)(m - 16) = mn

nm + 4m - 16n - 64 = mn

4m - 16n - 64 = 0

4m = 16n + 64

m = 4n + 16

And, had there been 4 fewer people, everyone would have received $24 more:

(n - 4)(m + 24) = mn

nm - 4m + 24n - 96 = mn

-4m + 24n - 96 = 0

-4m = -24n + 96

m = 6n - 24

Since m = 4n + 16 and m = 6n - 24, we have:

4n + 16 = 6n - 24

40 = 2n

20 = n

Answer: C

dave13 : You're so close!

I can't tell where your calculations went wrong, but your original equations are fine.

"N" value in both of your calculations, after you set up the equations, is incorrect. See below.

Just to make it clearer, I have substituted, for X, that which equals your X: Ny (# of people * amt per person = total amt).

X = Ny. Substitute Ny for X on LHS.

First:
\(\frac{Ny}{(n+4)}\) = (y - 16)
Ny = (N + 4)(y - 16)
Ny = Ny - 16N + 4y - 64
0 = -16N + 4y - 64 (i)

Second:
\(\frac{Ny}{(n-4)}\) = y + 24
Ny = (N - 4)(y + 24)
Ny = Ny + 24N - 4y - 96
0 = 24N - 4y - 96 (ii)

Add (ii) and (i)

24N - 4y - 96
-16N + 4y - 64
-----------------
8N - 160
8N = 160
N = 20

Hope that helps.

Total amount is same in each case :
(X+4)*16 = (x-4)*24
solve for X ..
It will come 20

4 people get
16+42=40.

1 people get 40÷4=10
So answer will be multiple of 10.
Here only C is multiple of 10.that's answer.

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