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To celebrate a colleague's retirement, the T coworkers

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To celebrate a colleague's retirement, the T coworkers [#permalink] New post 07 Dec 2012, 20:33
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To celebrate a colleague's retirement, the T coworkers in an office agreed to share equally the cost of a catered lunch. If the lunch costs a total of x dollars and S of the coworkers fail to pay their share, which of the following represents the additional amount, in dollars, that each of the remaining coworkers would have to contribute so that the cost of the lunch is completely paid?

A. x/T
B. x/(T-S)
C. Sx/(T-S)
D. Sx/T(T-S)
E. X(T-S)/T
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Re: To celebrate a colleague's retirement, the T coworkers [#permalink] New post 07 Dec 2012, 20:45
Cost of lunch = x
Number of People = T

If all joined in to pay, each will pay \frac{x}{T}
But that did not happen, only T-S paid. Thus, each who paid contributed \frac{x}{T-S}

\frac{x}{T-S}-\frac{x}{T} --> extra amount they paid because S are stingy..
\frac{xT - xT + xS}{(T)(T-S)}
\frac{xS}{T(T-S)}

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Re: To celebrate a colleague's retirement, the T coworkers [#permalink] New post 07 Dec 2012, 20:51
apoorvarora wrote:
To celebrate a colleague's retirement, the T coworkers in an office agreed to share equally the cost of a catered lunch. If the lunch costs a total of x dollars and S of the coworkers fail to pay their share, which of the following represents the additional amount, in dollars, that each of the remaining coworkers would have to contribute so that the cost of the lunch is completely paid?

A. x/T
B. x/T-S
C. Sx/T-S
D. Sx/T(T-S)
E. X(T-S)/T


Initial BURDEN on each coworker--->Total cost/ Number of Coworkers

or X/T

Now, when S coworkers are not paying their share, naturally the BURDEN on each coworker will increase in they have to raise their share in the total cost.
S are not paying their share, so # of coworkers who are willing to pay= T-S

Final BURDEN on each coworker----->Total cost/(T-S)

or X/(T-S)

Subtract the smaller from the larger.

X/(T-S) - X/T = XS/[T*(T-S)] .
Hope that helps.
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Re: To celebrate a colleague's retirement, the T coworkers [#permalink] New post 08 Dec 2012, 05:18
apoorvarora wrote:
To celebrate a colleague's retirement, the T coworkers in an office agreed to share equally the cost of a catered lunch. If the lunch costs a total of x dollars and S of the coworkers fail to pay their share, which of the following represents the additional amount, in dollars, that each of the remaining coworkers would have to contribute so that the cost of the lunch is completely paid?

A. x/T
B. x/T-S
C. Sx/T-S
D. Sx/T(T-S)
E. X(T-S)/T


I went with substitution method...
I replaced variables with values for easy calculations :-D

let
T =10
X= 200
s =2

Actual each person share 200/10 = 20

But 2 members didnt pay , so 8 members (T-S) would have paid the balance...
200/8 =25

25-20 = 5 Only choice D gives value same value..
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Re: To celebrate a colleague's retirement, the T coworkers [#permalink] New post 08 Dec 2012, 05:51
apoorvarora wrote:
To celebrate a colleague's retirement, the T coworkers in an office agreed to share equally the cost of a catered lunch. If the lunch costs a total of x dollars and S of the coworkers fail to pay their share, which of the following represents the additional amount, in dollars, that each of the remaining coworkers would have to contribute so that the cost of the lunch is completely paid?

A. x/T
B. x/(T-S)
C. Sx/(T-S)
D. Sx/T(T-S)
E. X(T-S)/T


Pick some smart numbers.

Let T=3, x=$3 and S=2.

So, we'd have that originally 3 coworkers were to pay $1 each for $3 lunch but 2 coworkers fail to pay, thus the remaining worker should pay additional $2 to cover the cost of the lunch.

Now, substitute T=3, x=$3 and S=2 into the answers to see which yields $2. Only answer D works.

Answer: D.
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Re: To celebrate a colleague's retirement, the T coworkers   [#permalink] 08 Dec 2012, 05:51
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