The real per capita GDP in country X is 4 times of that in country Y. The annual growth rate in country X is 2.33%, while in country Y it is 7%. How many years will it take for country Y to catch up to the real per capita GDP of country X?

It will take 30 years for country Y's GDP to catch up with that of country X

Explanation:

In this question. We are asked to calculate the number of years it will take a certain country Y to catch up with the GDP of a certain country X, given the annual growth rate in both countries.

We calculate the number of years as follows;

Firstly, we assign a variable to the value of the real GDP of country Y

let real

Let the real GDP of the country Y be n. This means that the GDP of country C will be 4 * n = 4n

With a 7% growth rate annual, country Y's Real GDP will be doubled in 70/7 = 10 years and;

With annual growth rate of 2.33%, country x's Real GDP doubles in 70/2.33 = 30 years. (Approx)

Now in next 30 years x's Real GDP will be = 2x4n = 8n

and Y's Real GDP in next 30 years will be = 2x2x2xn = 8n.

thus, it will take 30 years to country Y to catch up to the level of country x.