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Question

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

A
45 years
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B
40 years
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C
50 years
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D
Cannot be determined
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E
None of these
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Solution

## The correct option is C 50 yearsHere, Raman's present age = x yearsIt is given that Raman's present age =3× daughter's present age ∴ His daughter's present age =x3 yearsAnd, it is also given that Raman's present age =913× mother's present age His mother's present age =13x9 yearsAnd, Sum of their ages =125 ∴x+x3+13x9=125 ⇒9x+3x+13x9=125⇒25x9=125⇒x=125×925⇒x=45 yearsSo, Raman's present age =x=45 years∴ His daughter's present age =x3=453=15 yearsHis mother's present age =13x9=13×459=65 yearsSo, the difference between Raman's daughter's present age and Raman's mother's present age =65−15=50 years

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