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“Parts proportional to 2 and 3” means that one “part” is 2X, the other is 3X, where X is an unknown number.

“60 divided into two parts” sounds vague to me. Divide by two factors, or two summands?

If we are talking about multipliers, then 2X × 3X=60. We get X is equal to the root of 10, that is, there are no integer solutions.

For terms, 2X+3X=60. We get X=12, and the “parts” are 24 and 36, as in the last version.

Well, having ready-made answer options, you can stupidly reject everything where the “parts” do not give 60 (in total or in the product), and from the remaining ones – everything where the “parts” do not relate as 2:3 or 3:2. Again, 24 and 36 will remain.

Let's solve the simplest equation:

2x+3x=60

5x=60

x=12.

One number is 2x=24; the second is 3x=36.

Check: 24+36=60.

A problem from the fifth grade, or what?)

Answer: d) 24 and 36.