Problems On Ages

1. The Ratio of Ages of Mona and Sona is 4:5. Twelve Years hence, their ages will be in the ratio of 5:6. What will be Sona's age after 6 years ?

Sol: Let their present ages be 4x & 6x

Then (4x + 12)/(5x + 12) = 5/6 or x=12

Sona's age after 6 years = (5x +6) = 66 years

2.Ramu was 4 times as old as his son 8 years ago. After 8 years, Ramu will be twice as old as his son. What their present ages ?

Sol : Let son's age 8 years ago be x years

Then Ramu's age at that time = 4x years

Son's age after 8 years = (x +8) + 8 = (x + 16) years

Ramu's age after 8 years = (4x + 8) + 8 = (4x + 16) years

2(x + 16) = 4x + 16 or x=8

Son's present age = (x + 8) = 16 years

Ramu's present age= (4x + 8) = 40 years

3. A man is four times as old as his son. Five years ago, the man was nine times as old his son was at that time. What is the present age of a man ?

Sol : Let son's age = x, then man's age =4x.

9(x - 5) = (4x-5) or x=8.

Man's present age = (4x + 7) = 35 years

4. The sum of ages of Aruna and her mother is 49 years. Also, 7 years ago, the mothers age was 4 times Aruna's age. Find the present age of Aruna's mother.

Sol : Let Aruna's age 7 years ago be x.

Mother's age 7 years ago = 4x

(x + 7) + (4x + 7) =49 or x=7

Mother's present age = (4x + 7) = 35 years

5. The ages of A and B differ by 16 years. If 6 years ago, the elder one be 3 times as old as the younger one, find their present ages.

Sol : Let A's age = x & B's age = (x + 16)

3(x - 6) = (x + 16 - 6) or x=14

A's age = 14 years & B's age = 30 years.