Ratio

[Ashetty]

Please help me with attached ration problem.Thanks

[GMATGuruNY]

The ratio of the amount of Alex's fuel oil bill for the month of February to the amount of his fuel oil bill for the month of January was 3/2. If the fuel oil bill for February had been $40 more, the corresponding ratio would have been 5/3. How much was Alex's fuel oil bill for January?

A. $240
B. $300
C. $360
D. $450
E. $540

We can plug in the answers, which represent the amount in January.

Answer choice C: J=360.
3/2 = F/360
F = 540.
F+40 = 580.
580:360 = 29:18.
29:18 < 5:3.
Eliminate C.

The resulting ratio is too small.
The $40 being added to F needs to have more impact.
Thus, F and J have to be smaller.
To illustrate:

Let F=3000 and J=2000.
F+40 = 3040.
New F:J = 3040:2000. A very small increase in the ratio.

Let F=3 and J=2.
F+40 = 43.
New F:J = 43:2. A very big increase in the ratio.

Thus, to yield a bigger increase in the ratio, F and J must be smaller.
Eliminate D and E.

Answer choice B: J=300.
3/2 = F/300
F = 450.
F+40 = 490.
490:300 = 49:30.
49:30 < 5:3.
Eliminate B.

The correct answer is A.

For the curious, here's answer choice A:
3/2 = F/240
F = 360.
F+40 = 400.
New F:J = 400:240 = 5:3.