Correct Answer - Option 1 : 10 year
Solution :
Given :
Two years ago the son celebrated his tenth birthday ∴ Present age of the son = (10 + 2) years = 12 years
Calculations :
Let the present age of Father , Son and Daughter be F , S and D respectively.
Also the ratio of age of son to father six year from now is 3 : 7
Six year from now the ages of father and son be (F+6) and (S+6) respectively.
⇒ (S+6)/(F+6) = 3/7 ----(1)
⇒ Putting S = 12, in equation (1),
⇒ (12 + 6)/(F+6) = 3/7
⇒ 3 F + 18 = 126
⇒ F = 36 years
It is given that, the sum of present ages of son and daughter is 14 years less than the father’s age.
⇒ S + D = F – 14 ----(2)
Putting S = 12 and F = 36 in equation (2),
⇒ 12 + D = 36 – 14
⇒ D = 36 – 14 – 12
⇒ D = 10 years
Hence the present age of daughter is 10 years.