Multiple choice

The sum of the ages of husband and wife at present is 100. Ten years ago, the ratio of their ages was 9 : 7. What is the age of the husband?

  1. 45 years

  2. 55 years

  3. 65 years

  4. 40 years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let H and W be present ages. H+W=100. Ten years ago, (H-10)/(W-10) = 9/7. 7H - 70 = 9W - 90 => 7H - 9W = -20. Since W = 100-H, 7H - 9(100-H) = -20 => 7H - 900 + 9H = -20 => 16H = 880 => H = 55.

AI explanation

Let the present ages of the husband and wife be 9x and 7x respectively, reflecting their ages ten years ago when their ratio was 9 to 7. Ten years ago, their combined age was 100 minus 20, which equals 80. Therefore, 9x + 7x equals 80, making 16x equal 80 and x equal to 5. The husband's present age is 9x + 10, which calculates to 45 + 10, resulting in 55 years.

Keep practicing — related questions