Formulas For Ages

Question and Answer

Question 1: Saina Nehwal is 8 years older than her cousin. Her cousin is 24 years younger than his mother. If the ratio between the ages of Saina and her cousin’s mother is 7 : 11. What will be the age of Saina’s cousin after 3 years?

A. 21 years
B. 20 years
C. 26 years
D. 23 years

Answer: 23 years
Let the age of Saina = x, her cousin’s age = x – 8, Cousin’s mother age = x – 8 + 24
Ratio between the ages of Saina and her cousin’s mother is 7 : 11
x : x + 16 = 7 : 11
11 × x = (x + 16) × 7
11x = 7x + 112
4x = 112
x = 28
Saina’s cousin age = 28 – 8 = 20
After 3 years Saina’s cousin age = 20 + 3 = 23 years

Question 2 : Tiger’s present age is acquired, if we subtract 9 years from Arav’s present age and divide the remainder by 14. If Mohan’s age is 8 years and he is 3 years elder to Arav, then find Tiger’s present age.

A. 42
B. 79
C. 77
D. 85

Answer : 79 years
Explanation:
Let Tiger’s present age be x
Given, Mohan’s present age 8 years
Then, Arav’s present age = 8-3 = 5 years
Given, if we subtract 9 years from Arav’s present age and divide the remainder by 14 we will get Tiger’s present age
= x-9/14 = 5
x-9 = 70
x = 79 years
Tiger’s present is 79 years

Question 3 : Erika was five times older than Gigi ten years ago. The age of an Erika will be twice that of a Gigi in five years. How old were Erika’s compared to Gigi five years ago?

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

Answer : 3:1
Explanation :
Erika was 5 times older than Gigi 10 years ago.
Let the age of Gigi 10 years ago be x years.
∴ The age of Erika 10 years ago = 5x years
5 years from now, Erika will be twice older than Gigi.
∴ We can write now,
(5x + 10 + 5) = 2 × (x + 10 + 5)
⇒ 5x + 15 = 2x + 30
⇒ 3x = 15
⇒ x = 5
∴ Age of Gigi 10 years ago = 5 years
And, the age of Erika 10 years ago = 5x = 5 × 5 = 25 years
∴ The reqd. ratio = \frac{25 + 5}{5+5} = \frac{30}{10} = 3:1

Question 4 : Sum of the ages of Tendulkar and Dravid 16 years hence will be equal to 3 times their present age. If at present Tendulkar is 10 years elder to Dravid, then what are their present ages?

A. 22, 8
B. 29, 12
C. 13, 3
D. 13, 6

Answer: 13, 3
Let the present ages of Tendulkar and Dravid be x years and y years respectively.
As per the question,
(x + 16) + (y + 16) = 3(x + y)
x + y + 32 = 3x + 3y
x + y = 16 …..(i)
Also,
y + 10 = x
x – y = 10 …..(ii)
Solving eqns (i) and (ii), we get
x = 13 and y = 3
Therefore, Present ages of Tendulkar and Dravid is 13 years and 3 years respectively.

Question 5 : Amitabh said to his friend “If you subtract 18 from my age the two digits of my age will reverse their positions. Also my age is six, less than 8 times the sum of digits of my age”. Find Amitabh’s age.

A. 46 years
B. 37 years
C. 56 years
D. 42 years

Answer:
Let Mayank’s age be (10x + y) years
Age by reversing the digits = (10y + x) yrs
Now, 10x + y − 18= 10y + x
9x – 9y = 18
x – y = 2………………(1)
Also,
10x+y = 8(x+y) – 6
2x – 7y = –6……….… (2)
Solving equations (1) and (2),
x = 4 , y = 2
Therefore, Mayank’s age = 10x + y
= 10(4) + 2
= 42 years