While on a holiday, X persons have decided to rent a van. The rent of the van is Tk D and each person is to pay an equal share. If Y persons cancel their trip, which of the following represents the additional amount of Tk per person that each remaining person must pay in order to still rent the van?

Question: While on a holiday, X persons have decided to rent a van. The rent of the van is Tk D and each person is to pay an equal share. If Y persons cancel their trip, which of the following represents the additional amount of Tk per person that each remaining person must pay in order to still rent the van?

Solution:
Total rent = Tk. D
Original number of persons = X
∴ Original share per person = D/X

And,
If Y persons cancel then,
∴ Remaining persons = X - Y
∴ New share per person = D/(X - Y)

∴ Additional amount each remaining person must pay = {D/(X - Y)} - (D/X)
= D{1/(X - Y)} - (1/X)}
= D{(X - X + Y)/X(X - Y)}
= YD/(X(X - Y))

∴ The additional amount per remaining person is YD/(X(X - Y)).