MathematicsTwo years ago, Ram was thrice as old as his daughter and six years later, he will be four years older than twice her age. How old are they now?

Two years ago, Ram was thrice as old as his daughter and six years later, he will be four years older than twice her age. How old are they now?


  1. A
    30 years and 10 years
  2. B
    52 years and 19 years
  3. C
    41 years and 12 years
  4. D
    38 years and 14 years 

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    Solution:

    Given that two years ago, Ram was 3 times older than his daughter and after six years he will be 4 years older than twice her daughter. We need to find the present age of Ram and his daughter.
    Let the present of Ram and his daughter be x years and y years.
    Now, two years ago, Ram was 3 times older than his daughter, therefore, we have,
    x2=3(y2) x2=3y6 x=3y4...(i)  
    After six years he will be 4 years older than twice her daughter,
    x+6=2(y+6)+4 x+6=2y+12+4 x2y=166 x2y=10...(ii)  
    Now, substituting the value of x from equation (i) in equation (ii),
    (3y4)2y=10 3y42y=10 3y2y=10+4 y=14  
    Now, substituting the value of y in equation (i), we have,
    x=3 14 4 x=424 x=38  
    Thus, the present age of Ram is 38 years and of his daughter is 14 years.
    Therefore, option 4 is correct.
     
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