Multiple choice

The ratio of the ages of Rajiv and Raghu is 5 : 7 when the age of their father is 50 years. The difference between the ages of Rajiv and Raghu is 8 years. What will be the age of their father, when the ratio of their ages is 2 : 3?

  1. 42 years

  2. 44 years

  3. 46 years

  4. 48 years

  5. 52 years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Since the difference between Rajiv's and Raghu's ages is 8 years and their ratio is 5 : 7, their ages are 20 and 28 respectively when their father is 50. To find when their ratio is 2 : 3, we solve (20 + y)/(28 + y) = 2/3, which gives y = -4, meaning this occurred 4 years ago when the father was 46 years old.

AI explanation

The difference between Rajiv's and Raghu's ages is a constant 8 years, so when their ratio is 5 : 7, the difference of 2 parts equals 8 years, making each part 4 years. This means their current ages are 5 times 4 equal to 20 years and 7 times 4 equal to 28 years, summing to 48 years. Since the father is currently 50 years old and the sum of the sons' ages is 48, the father is 2 years older than the sum of their ages. When the ratio of the sons' ages becomes 2 : 3, the difference of 1 part equals 8 years, meaning their ages will be 16 and 24, which sum to 40. Therefore, the father's age will be 40 plus 2, which is 46 years.

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