Multiple choice

Raman's present age is thrice his daughter's age and 9/13 of his mother's present age. The sum of the present ages of all three of them is 125 years. What is the difference between the present ages of Raman's daughter and Raman's mother?

  1. 45 years

  2. 50 years

  3. 40 years

  4. Cannot be determined

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let D be the daughter's age, R be Raman's age, and M be his mother's age. R = 3D and R = (9/13)M. Thus, M = (13/9)R = (13/9)(3D) = (13/3)D. The sum D + R + M = 125, so D + 3D + (13/3)D = 125. Multiplying by 3 gives 3D + 9D + 13D = 375, so 25D = 375, D = 15. Then R = 45 and M = 65. The difference M - D = 65 - 15 = 50.

AI explanation

Let the daughter's age be 9x, making Raman's age 27x, and the mother's age 39x. The sum of their ages is 125, giving the equation 9x plus 27x plus 39x equals 125. This simplifies to 75x equals 125, so x equals 5 over 3. The difference between the ages of the daughter and the mother is 39x minus 9x, which is 30x, and multiplying this by 5 over 3 gives 50 years.

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