Let us go through some problems on ages (with solutions) to understand the concept and statements of ages in a better manner.
Example 1: 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.
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Sol: 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.
Example 2: 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.
Sol: 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.
Example 3: 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.
Sol: 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.
Example 4: Farookh is aged twice more than his son Raunak. After ten years, he would be twice Ronit’s age. What are there present ages?
Sol: 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.
Example 5: The sum of ages of five children born at the intervals of four years each is 80 years. Find the age of the youngest child?
Sol: Let the ages of children be y, (y + 4), (y + 8), (y + 12) and (y + 16) years.
Then, y + (y + 4) + (y + 8) + (y + 12) + (y+ 16) = 80 ⇒ 5y = 40 ⇒ y = 8.
So the age of the youngest child y = 8 years.
Example 6: Presently, the ratio of ages of Sandeep and Amrit is 6: 5. Five years hence, the ratio of their ages will become 7:6 respectively. What is Amrit's present age in years?
Sol: Let the present ages of Sandeep and Amrit be 6x & 5x years respectively.
As per the question, (6x+5) / (5x+5) = 7/6 ⇒ 6(6x + 5) = 7(5x + 5) ⇒ 36x + 30 = 35x + 35
⇒ 36x - 35x = 35 – 30 ⇒ x = 5. ∴ Amrit's present age = 5x = 30 years.
Example 7: Akshay is three years older than Bomkesh, who is twice as old as Chintu. If the sum of the ages of Akshay, Bomkesh and Chintu is 53 years, then how old is Bomkesh?
Sol: Let Chintu's age be x years. Then, Bomkesh's age = 2x years. Hence Akshay's age = (2x + 3) years.
∴ (2x + 3) + 2x + x = 53 ⇒ 5x = 50 ⇒ x = 10. Hence, Bomkesh's age = 2x = 20 years.