Problem Solving

Hello

Can someone plz point out my mistake. I think that considering we have a single constant for the equation I can add the linear equations up. But the OA is far away from my answer.

Thanks

The OA is 1900

x is directly proportional to y means the following:
x = ky, where k is a constant.

In the problem above, let n = the number of occupants, v = the variable expense, and c = the constant expense.
Total expenses = v + c.

Since the variable expense is directly proportional to the number of occupants, we get:
v = kn.
Thus:
Total expenses = kn + c, where n is the number of occupants, and k and c are constants.

200 occupants:
Total expenses = kn + c.
1300 = 200k + c.

250 occupants:
Total expenses = kn + c.
1600 = 250k + c.

Subtracting the first equation from the second, we get:
1600-1300 = (250k + c) - (200k + c)
300 = 50k
k = 6.

Substituting k=6 into 1300 = 200k + c, we get:
1300 = 200*6 = c
c = 100.

Total expenses for 300 inmates:
Total = kn + c = 6*300 + 100 = 1900.

I solved it in a similar way

200 --> 1300
250 --> 1600

An increase of 50 inmates = an increase of RS 300
An increasse of 100 (50*2) inmates = 2 * (increase of RS300) = 1300 + 600 = 1900