SECTION B: DATA INTERPRETATION AND QUANTITATIVE ABILITY

 

73. Raj Travels has the following revenue model for a group package. Owner charges Rs.20,000 per person till group size of 200. For every additional traveller beyond 200, he starts offering discount of 50 rupees to all members of the group. The maximum possible income for Raj travels from the package is:

A.  Rs.4000000                 B.  Rs.4200000                C.  Rs.4500000                 D.  Rs.5000000                E.  Rs.5500000

 

Solution:

Let the number of additional travellers over 200 be n.

      Income = (200 + n) (20,000 – 50n)

      I = 400000 + 10000 n – 50n2

      For maximum income

      I = 50 [80000 + (200n – n2)]

      I = 50 [90000 – (n – 100)2]

(n – 100)2 must be minimum for I to be maximum.

(n – 100)2 cannot be negative the minimum value is 0, when n = 100.

      \ I = 4500000 – 50(n – 100)2.

      Hence Imax = 4500000                                                                                                                                 Choice (C)