Question

In 1870, the U.S had an average income of about $2758 and the U.K of about $3463. In 1999, the figures were $30,600 and $22,640, respectively. If each country grew at a constant rate over these years, in which year did the U.S. overtake the U.K. in terms of average income?

Answer 1

Given Data: In 1870, the U.S had an average income of about $2758 and U.K of about $ 3463.

• ​​​Difference in years = 1999 - 1870 = 129 years.
• Growth rate in each year of u.s = increase in income / difference in years =($30600 - $2758)/129 = $215.829 per year.
• Growth rate in each year of U.K = increase in income / difference in years = ($22640- $3463)/129 = $148.658 per year.
• Let 'X' be the no. of years for equal income in U.S and U.K.

Required equation of equal income as below:

U.S. income = U.K. income

$2758 + ( X * $215.829) = $3463 + ( X * $148.658)

$67.171 X = $705

X = 10.49 years.

At 10.49th year both the income will be same.

Therefore, at 11th year U.S. income will exceed U.K. income.