Problems on Ages

Introduction

When you have to calculate the age of persons based on the given information, you may have to be careful and think twice before you give out the answer. Since there can only be a limited number of options for the answer, you must analyze the data carefully and find that option that is most likely to be correct. Problems on age is a common topic asked in government exams and UG level exams including CLAT, AILET, etc. Candidates with a good grip on this topic can easily score well in this section.

Age-based questions are generally asked in three aspects: past, present, and future. 

• Problems based on basic mathematical operations

1. Rahul’s age after 15 years will be five times his age five years back. What is the present age of Rahul? 

Ans. Let Rahul’s present age be x years. Then,

Rahul’s age after 15 years = (x + 15) years. Rahul’s age 5 years back = (x – 5) years.

x + 15 = 5 (x – 5) ⇒ x + 15 = 5x 25 4x = 40 x = 10. Hence, Rahul’s present age = 10 years.

2. The product of the ages of Ankita and Nikita is 240. If twice the age, Nikita is more than Ankita’s age by four years, what is Nikita’s age?

Sol. Let Ankita’s age be x years. Then, Nikita’s age = 240 x years.

2x 240 – x = 4 480x² = 4x ⇒ x² + 4x – 480 = 0

⇒ (x+24) (x-20) = 0 ⇒ x = 20.

Hence, Nikita’s age =(240/20) years = 12 years.

• Problems based on Ratios

1. One year ago, the ratio of Gaurvi and Sachin’s age was 6: 7, respectively. Four years hence, the ratio would be 7: 8. How old is Sachin? 

Ans. Let Gaurvi and Sachin’s ages are 6x and 7x years, respectively. Then, Gaurvi’s age is 4 years hence = (6x + 1) + 4 = (6x + 5) years.

 Sachin’s age is 4 years hence = (7x + 1) + 4 = (7x + 5) years.

6x + 5/ 7x+5= 7 /8

 8 (6x + 5) = 7 (7x + 5) ⇒ 48x + 40 = 49x +35 x = 5,

Hence, Sachin’s present age = (7x + 1) = 36 years.

2. Abhi’s age after six years will be three-seventh of his father’s age. Ten years ago, the ratio of their ages was 1: 5. What is Abhi’s father’s age at present?

Sol. Let the ages of Abhi and his father 10 years ago be x and 5x years respectively. Then, Abhi’s age after 6 years = (x + 10) + 6 = (x + 16) years. 

Father’s age after 6 years = (5x + 10) + 6 = (5x + 16) years.

Therefore, (x+16) = 3/7(5x+16)

7 (x + 16) = 3 (5x + 16) ⇒ 7x + 112 = 15x + 48

8x =64, x = 8.

Hence, Abhi’s father’s present age = (5x + 10) = 50 years.

Directions Mark (✔) against the correct answer :

1. Sachin is younger than Rohan by four years. If their ages are in the respective ratio of 7:9, how old is Sachin? 

1. 16 years
2.  28 years
3. 18 years
4. None of these

2. The ratio between the present ages of X and Y is 6: 7. If Y is four years older than X, what will be the ratio of the ages of X and Y after four years? (S.B.I.P.O. 1998)

1. 3:4
2. 3:5
3. 4:3
4. None of these

3. The ratio between the present ages of and B is 5:7 respectively. If the difference between B’s present age and A’s age after six years is 2, what is the total of A’s and B’s present ages? (Bank P.O. 1999)

1. 48 years
2. 52 years
3.  56 years
4. None of these

4. At present, the ratio between the ages of Arundhati and Diksha is 4:3. After six years, Arundhati’s age will be 26 years. What is the age of Diksha at present?

1. 12 years
2. 15 years
3. 19 ½ years

      (d) 21 years

5. My sister is three years older than me. My mother was 28 years of age when my brother was born, while my father was 26 years of age when I was born. If my brother was four years of age when my sister was born, then what was the age of my mother and father respectively when my sister was born?

1. 32yrs, 23 yrs
2. 32yrs, 39 yrs
3. 35 yrs, 29 yrs

      (d) 35 yrs, 33 yrs

ANSWERS

1. D
2. D
3. A
4. B
5. A

Conclusion

The most important thing to remember while learning or practicing age problems is that they are formed in the same way as a normal linear equation. You need to consider the age and years of one person and then vary it concerning another person. Make sure you solve it, considering that an older person is always there before a younger person in the given question. Whenever you solve a word problem based on age, make sure you cover the basic points of formulating the equation and how to solve it.