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C individuals pledged to pay equal contributions so that a charity...

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C individuals pledged to pay equal contributions so that a charity...  [#permalink]

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New post 28 Jul 2016, 08:41
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Question Stats:

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C individuals pledged to pay equal contributions so that a charity’s goal of $x could be reached. If d of the contributors failed to pay their share, which of the following represents the additional number of dollars that each of the remaining individuals would have to pay in order to allow the charity to reach its goal?

A) dx / C
B) x / (C-d)
C) d / (C-dx)
D) x / (C(C-d))
E) dx / (C(C-d))

Please develop in detail your answer.

Thank you.
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Re: C individuals pledged to pay equal contributions so that a charity...  [#permalink]

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New post 28 Jul 2016, 09:12
Number of individuals = C
Amount paid by each individual = n
Total expected amount = Charity's goal = nC = x
n = x/C

Number of individuals who fail to pay = d
Contribution from individuals who would fail to pay = dx/C --> Additional amount

Number of individuals who are paying = C - d
Additional amount has to be divided among the (C - d) individuals --> dx/C(C - d)

Answer: E
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Re: C individuals pledged to pay equal contributions so that a charity...  [#permalink]

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New post 29 Jul 2016, 02:05
c people would pay x

1)so contra would be =x/c

2)but d people refused or didn't pay , so for same x contra increased to =x/(c-d)

note 2 nd point above has more contribution than 1 point above

so increase in contri is 2 statement - 1 statement above

x/c-d - x/c which will give you E as answer
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Re: C individuals pledged to pay equal contributions so that a charity...  [#permalink]

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New post 06 Aug 2016, 01:43
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EBITDA wrote:
C individuals pledged to pay equal contributions so that a charity’s goal of $x could be reached. If d of the contributors failed to pay their share, which of the following represents the additional number of dollars that each of the remaining individuals would have to pay in order to allow the charity to reach its goal?


\(\frac{x}{C} \text{ - original cost}\\
\frac{x}{C-d} \text{ - new cost}\\
\text{additional cost = new cost - original cost}\\
\frac{x}{C-d} - \frac{x}{C} = \frac{x(C)}{C(C-d)} - \frac{x(C-d)}{C(C-d)} = \frac{xd}{C(C-D)}\)

E) dx / (C(C-d))
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Re: C individuals pledged to pay equal contributions so that a charity...  [#permalink]

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New post 29 Jan 2018, 10:56
EBITDA wrote:
C individuals pledged to pay equal contributions so that a charity’s goal of $x could be reached. If d of the contributors failed to pay their share, which of the following represents the additional number of dollars that each of the remaining individuals would have to pay in order to allow the charity to reach its goal?

A) dx / C
B) x / (C-d)
C) d / (C-dx)
D) x / (C(C-d))
E) dx / (C(C-d))


Had all C individuals paid their contributions, each would have paid x/C dollars. Since d of them failed to pay theirs, each of the remaining individuals would now have to pay x/(C - d) dollars. Thus, the difference in the number of dollars contributed by each person is:

x/(C - d) - x/C

Obtaining the common denominator C(C - d), we have:

xC/[C(C - d)] - x(C - d)/[C(C - d)]

[xC - x(C - d)]/[C(C - d)]

(xC - xC + xd)/[C(C - d)]

xd/[C(C - d)]

Answer: E
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C individuals pledged to pay equal contributions so that a charity...  [#permalink]

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New post Updated on: 07 Dec 2018, 23:58
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Algebraic solutions are already there, so Lets do it by assuming some values-

whenever you have to assume some values, make sure they in multiple.
It becomes easy to calculate later.


say x=$100, c=10, d=5

to reach $100, 10 people have to contribute $10 each.
5 of them did not give their share= 50$ was short
this $50 must be shared by remaining 5 people.

additional share the remaining people have to share= 50/5= $10

we have x=$100, c=10, d=5, and our right answer should give you $10 after putting values of x,c and d.

E gives $10 as answer.

SO E is the correct answer.
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Originally posted by aa008 on 07 Dec 2018, 21:36.
Last edited by aa008 on 07 Dec 2018, 23:58, edited 1 time in total.
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Re: C individuals pledged to pay equal contributions so that a charity...  [#permalink]

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New post 07 Dec 2018, 23:56
EBITDA wrote:
C individuals pledged to pay equal contributions so that a charity’s goal of $x could be reached. If d of the contributors failed to pay their share, which of the following represents the additional number of dollars that each of the remaining individuals would have to pay in order to allow the charity to reach its goal?

A) dx / C
B) x / (C-d)
C) d / (C-dx)
D) x / (C(C-d))
E) dx / (C(C-d))

Please develop in detail your answer.

Thank you.


I've come up with a simple solution; Here is the logic that I used:
Total share of each person is \(x/C\). After failing \(d\) people to pay their shares, the total amount of their shares (\(dx/C\)) need to be paid by \(C-d\) individuals.
So, we get: \((dx/c)/(c-d)\) and hence \(dx/c(c-d)\), choice E.
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Re: C individuals pledged to pay equal contributions so that a charity...  [#permalink]

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New post 23 Nov 2019, 00:35
Let t be the amount each person has to pay. => C*t = x => t= C/x

now, let n be the amount each person has to pay extra.

=> (C-d)*(t+n) = x

Solving and substituting t=X/C we get n as dX/C(C-d)

Ans E
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Re: C individuals pledged to pay equal contributions so that a charity...   [#permalink] 23 Nov 2019, 00:35
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