Raman's present age is three times his daughter's and nine-thirteenth of his mother's present age. The sum of the present ages of all three of them is 125 yr. What is the difference between the present ages of Raman's daughter and Raman's mother?

45 yr
40 yr
50 yr
Connot be determined

Correct Answer: 50 yr

Explanation:

Let age of Raman's daughter = N yr
Then, age of Raman's = 3N yr
and age of Raman's mother = (13/9) x 3N = 13N/3 yr
According to the question, N + 3N + 13N/3 = 125
⇒ 3N + 9N + 13N = 125 x 3
∴ N = (125 x 3)/25 = 15
Hence, required difference = 13N/3 - N = 10N/3
= (10 x 15)/3 = 50 yr

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