Algebra-3 (Placement Q's)(GRE/GMAT Word problems)

A group of friends went for a dinner and got a bill of Rs 2400. They have decided to contribute equally for the bill. But two of them could not contribute and to compensate that, rest all contributed Rs 100 more. How many are there in the group?

(A) 6       (B)10        (C) 8        (D) 12

Solution follows here:

Solution:

Let there are ‘x’ members in the group.

If all those in the group contribute equally, let the contribution per head be ‘m’.

=> m * x = 2400                       ------(1)

But given, two of them could not contribute and to compensate that, rest all contributed Rs 100 more. This means, (x-2) contributed (m+100) each.

=> (m+100) * (x-2) = 2400   ------(2)

Instead of solving the two equations, we check for the given answer options one by one:

Option (A), put x=6 in equation (1), 6m = 2400 => m = 400

put x=6 in equation (2), (m+100)*4 = 2400 => m+100 = 600 => m = 500

both are contradicting each other, hence Option (A) is wrong

Option (B), put x=10 in equation (1), 10m = 2400 => m = 240

put x=10 in equation (2), (m+100)*8 = 2400 => m+100 = 300 => m = 200

both are contradicting each other, hence Option (B) is wrong

Option (C), put x=8 in equation (1), 8m = 2400 => m = 300

put x=8 in equation (2), (m+100)*6 = 2400 => m+100 = 400 => m = 300

yes, both give same result, hence Option (C) is correct. Answer is Option (C)