Problems on Ages

 

Problems on Ages

Concepts on solving problems on Ages
Case -1	Case-2	Case - 3
If Present age = x years (given)	If age n years ago or before = x years (given)	If age n years hence or after = x years (given)
Then,	Then,	Then,
n years ago or before, age = x - n	Present age = x + n	Present age = x - n
n years after or hence, age = x + n	m years after or hence, age = x + n + m	m years ago or before, age = x - n - m

       

1.  Present age of X and Y are in the ratio 5 : 6 respectively. Seven years hence this ratio will become 6 : 7 respectively. What is X’s present age in years?

Solutions :

X	Y
Present age = 5x 7 years hence, age = 5x + 7	Present age = 6x   7 years hence, age = 6x + 7

         So, (5x + 7) / (6x + 7) = 6 / 7

               ⟹35x + 49 = 36x + 42 ⟹ x = 7

                 Present age of X = 5x = 35 (Ans.)

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

Solutions:

Let son’s age 8 years ago = x years

Then Rohit’s age 8 years ago = 4x years

Present age of son = x + 8 ,  Rohit’s present age = 4x + 8

            After 8 years, son’s age = x + 8 + 8 = x + 16

            After 8 years, Rohit’s age = 4x + 8 + 8 = 4x + 16

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

                So, son’s present age = x + 8 = 16 years

               Rohit’s present age = 4x + 8 = 40 years (Ans.)

3.  In 10 years, A will be twice as old as B was 10 years ago. If A is now 9 years older than B, the present age of B is :______

Solution:

                Let age of B = x, then A = x + 9

                So, x + 9 + 10 = 2 (x − 10) ⟹ x = 39 years (Ans.)

 4. The difference between the ages of two persons is10 years. Fifteen years ago the elder one was twice as old as the younger one. The present age of elder person is :____

Solution:

                Let younger one’s age = x , then elder one’s age = x + 10

                15 years ago, younger = x – 15 and elder = x + 10 – 15 = x – 5

                      So, x – 5 = 2 (x − 15) ⟹ x = 25

                The present age of elder person = x + 10 = 35 (Ans.)

 

5.  The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages was 34. The ages of son and the father are respectively :____

Solution:

          Let son’s age = x, father age = 45 – x

          5 years ago, son’s age = x − 5, father age = 45 – x – 5 = 40 – x

           So, ( x – 5) × (40 – x) = 34 ⟹ x =  39 or 6

           Father’s age = 39 and son’s age = 6 (Ans.) 

Do it yourself

1. Father is four times the age of his daughter. If after 5 years, he would be three times of daughter’s age, then further after 5 years, how many times he would be of his daughter’s age? (Ans. 2.5 times)

2. Nisha is 15 years elder to Romi. If 5 years ago, Nisha was 3 times as old as Romi, then find Nisha’s present age. (Ans.27.5 years)

3. The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child? (Ans. 4 years)

4.  Sachin is younger than Rahul by 7 years. If their ages are in the respective ratio of 7 : 9, how old is Sachin? (Ans. 24.5 years)

5. The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years). (Ans. 16, 28, 36)

6. Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years? (Ans. 24 years)

7.  The ages of two persons differ by 16 years. If 6 years ago, the elder one be 3 times as old as the younger one, find their present ages. (Ans. 14 & 30 years)

8. A person’s present age is two-fifth of the age of his mother. After 8 years , he will be one-half of the age of his mother. How old is the mother at present? (Ans. 40 years)

9.      The ratio of the present ages two brothers is 1 : 2 and 5 years back, the ratio was 1 : 3. What will be the ratio of their ages after 5 years?  (Ans. 3 : 5)

10. A person's present age is three-fifth of the age of his mother. After 8 years, he will be two-third of the age of his mother. How old is mother at present? (Ans.40 years)

11. Father is 5 yr older than the mother and the mother's age now is thrice the age of the daughter. The daughter is now 10 yr old. What was the father's age when the daughter was born? (Ans.25 yr)

12. Twenty-two years ago, A was two-third of B in age. If the ratio of their present ages is 4:5, what will be the total of their present ages? (Ans.99 yr)

13. Twelve years ago, A was half of B in age. If the ratio of their present ages is 4:5, what will be the total of their present ages? (Ans.36 yr) 

14. The sum of the present age of mother and her son is 60 years. Six years ago, the age of the mother was five times the age of her son. What will be the age of her son after 6 years?

15. The product of the ages of Ankita and Nikita is 240. If twice the age of Nikita is more than Ankita's age by 4 years, what is Nikita's age? (Ans.12 years)

16. Ranita'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 Ranita's father's age at present? (Ans.50 years)

N.B – Specially focused on Bank P.O, Clerk, SSC and Sub-ordinate Staff Selection Examinations Papers.