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Math Expert V
Joined: 02 Sep 2009
Posts: 55618
An amount of money was divided between some people in such a way that  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 68% (02:52) correct 32% (02:51) wrong based on 74 sessions

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An amount of money was divided between some people in such a way that if there had been 4 more people, everyone would have $16 less. but if there had been 4 less people, everyone would have got$24 more. How many people were there in group? ?

A. 12
B. 16
C. 20
D. 24
E. 32

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Current Student P
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Posts: 618
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29 GMAT 2: 740 Q51 V38 Re: An amount of money was divided between some people in such a way that  [#permalink]

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Bunuel wrote:
An amount of money was divided between some people in such a way that if there had been 4 people, everyone would have $16 less. but if there had been 4 less people, everyone would have got$24 more. How many people were there in group? ?

A. 12
B. 16
C. 20
D. 24
E. 32

Let n be the number of people with p dollars
total = pn

(n+4)(p-16)=pn
np+4p-16n-64 = pn
4p-16n = 64.......(i)

(n-4)(p+24)=pn
-4p+24n = 96.......(ii)

on solving we get
8n = 160
n=20
C
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Joined: 13 Jul 2015
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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
Intern  B
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@ Brunel - I agree with dave13 .

I too assumed if there had been 4 more people in the first part of the problem.
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An amount of money was divided between some people in such a way that  [#permalink]

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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 ?
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As seen from pic. It is easily understandable.
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File comment: Solution IMG_5134.JPG [ 1.6 MiB | Viewed 2555 times ]

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Re: An amount of money was divided between some people in such a way that  [#permalink]

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Bunuel wrote:
An amount of money was divided between some people in such a way that if there had been 4 more people, everyone would have $16 less. but if there had been 4 less people, everyone would have got$24 more. How many people were there in group? ?

A. 12
B. 16
C. 20
D. 24
E. 32

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

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Senior SC Moderator V
Joined: 22 May 2016
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An amount of money was divided between some people in such a way that  [#permalink]

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dave13 wrote:
Bunuel wrote:
An amount of money was divided between some people in such a way that if there had been 4 people, everyone would have $16 less. but if there had been 4 less people, everyone would have got$24 more. How many people were there in group? ?

A. 12
B. 16
C. 20
D. 24
E. 32

Bunuel you know 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 ?

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)

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

Hope that helps.
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Joined: 14 Nov 2014
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Re: An amount of money was divided between some people in such a way that  [#permalink]

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Total amount is same in each case :
(X+4)*16 = (x-4)*24
solve for X ..
It will come 20
Intern  Joined: 07 Feb 2019
Posts: 13
Re: An amount of money was divided between some people in such a way that  [#permalink]

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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.

Posted from my mobile device Re: An amount of money was divided between some people in such a way that   [#permalink] 15 Mar 2019, 18:47
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