If a is increased by 50% and b is decreased by 50%, the resulting numbers will be equal. What is the ratio of a to b?

1:3

Step-by-step explanation:

To answer this, since the resulting numbers are equal, we can choose any arbitrary number for the resulting number.

Let the resulting number be 100.

As deduced from the question, A is increased by 50%, this means before the increment, A had a value of 66 (2/3), an increment of 33 (1/3) gave its present value.

Now, we were told that B was decreased by 50%, this means initially, B was at a value of 200.

Now the ratio of A to B is:

66 (2/3) to 200

Converting A to improper fraction will yield 200/3.

The ratio is thus

200/3 : 200

This is same as

1/3 : 1 or simply 1:3