Six year from now ratio of age of son to father is 3 : 7. The sum of p

1.	Six year from now ratio of age of son to father is 3 : 7. The sum of present ages of son and daughter is 14 years less than the father’s age. Two years ago, son celebrated his tenth birthday, Find the age of daughter.1. 10 year2. 12 year3. 15 year4. 17 year5. 13 year
Answer» 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.

Six year from now ratio of age of son to father is 3 : 7. The sum of present ages of son and daughter is 14 years less than the father’s age. Two years ago, son celebrated his tenth birthday, Find the age of daughter.1. 10 year2. 12 year3. 15 year4. 17 year5. 13 year

Answer» 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.