how much to pay if others didn't pay

[yuri]

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 amoun, 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

The correct one is d) and I event guessed it right , but guessing is a dangerous thingy in this business... Thank you!

[ri2007]

The original cost per person would have been X/T

Since S people did not pay the new cost per person would be X/T-S

The additional cost per person is (X/(T-S)) - X/T ....now since LCM which is T(T-S), you get

= XT/T(T-S) - X(T-S)/ T(T-S) = Sx/T(T - S)

[Suyog]

Try substituting simple values into these variables.

Say T = 25, Number of ppl decided to contribute
x = 100, Amount
s = 15, ppl failed to contribute

Earlier Contribution $4 each, 15 ppl failed so $10 each i.e. $6 more every person.

Now put these values in the given options.

a) 4...No
b) 10...No
c) 150...No
d) 6...gotchaa!!!
e) 40...No

Ans D.

[camitava]

Agree with ri2007 and I also follow the approach as taken by ri2007.

[yuri]

Thank you guys. I got freaked out on time, and when started subbing the numbers in it, picked simple numbers, but not the ones that work with the task, so I just guessed and moved on. THe score was good anyway, but I missed at least 4 problems, which are really basic, and should pop up right away. THank you all again!