In order to buy a car, a man borrowed 180,000 on the condition that he

This is not a good question for many reasons. For one, it's not clear how the interest rate is even applied - you'd normally assume that, as you pay off the principal, you'd pay interest on a lower and lower total amount. But that's not what's happening here, judging by the numbers in the question. Instead we're meant to apply the 7% and 7.5% interest rates to the initial loan amount of $180,000 every year, even when the person has paid off 95% of the principal. So all of the information about how he pays off the principal is irrelevant (except for the fact that it takes 21 years). The numbers in the question are also completely unlike the numbers you'd ever see in a GMAT question. What is the source?

Anyway, we can solve - if he pays 7.5% for n years, and then 7% for the remaining 21-n years on $180,000, then he pays this much interest:

(7.5/100)(180,000)(n) + (7/100)(180,000)(21 - n)

That's equal to $270,900, so we have:

(7.5/100)(180,000)(n) + (7/100)(180,000)(21 - n) = 270,900
(7.5)(1800)(n) + (7)(1800)(21 - n) = 270,900
7.5n + 147 - 7n = 270,900/1800 = 301/2
15n + 294 - 14n = 301
n = 7

So he invested 7 years at the higher interest rate, and 14 at the lower one, which is what the question asked us to find.