Let us go through some problems on ages (with solutions) to understand the concept and statements of ages in a better manner.
The ratio of the present ages of Supriya and her mother is 2:9. The mother's age at the time of Supriya’s birth was 28 years. Find their present ages.
Present ratio of ages between Supriya and her mother is 2: 9. ∴
Let the actual ages of Supriya and her mother be 2x and 9x. The age of her mother at the time of Supriya’s birth was 28 years. Therefore, the difference between Supriya and her mother's age will always remain 28 years.
∴ 9x – 2x = 28 ⇒ x = 4. Hence their present ages are 8 and 36 yrs.
The ratio of the present ages of John and Jim is 4:3. Six years hence it will be 5: 4. Find the present ages.
Present ratio = 4: 3. ∴ Actual ages are 4x and 3x. So (4x+6) / (3x+6) = 5/4 ⇒ x = 6
So their present ages are 24 yrs and 18 yrs.
Presently, the ratio of the ages of Chintu and Mintu is 7: 12. Two years ago, the ratio was 3:8. Find their current ages.
Present ratio = 7: 12. Actual ages are 7x and 12x.
∴ (7x - 2) / (12x - 2) = 3/8
⇒ x = 0.5. So actual ages are 7(0.5) = 3.5 years and 12 (0.5) = 6 years.
Farookh is aged twice more than his son Raunak. After ten years, he would be twice Ronit’s age. What are there present ages?
Let Raunak's present age be x years. Now the Farookh is given to be twice more i.e. then, Farookh's present age =(x + 2x) years = 3x years.
As per the question, (3x + 10) = 2/1(x+10) ⇒ 3x + 10 = 2x + 20 ⇒ x = 10.
Hence age of Raunak = 10 years and hence his Farookh’s present age is 30 years.