# Problems On Ages (concepts & Related Solved Problems)

Problems on Ages (Quick Tips and Tricks)

1) If the current age of a person be X, then

- age after n years = X + n

- age n years ago = X – n

- n times the age = nX

- If ages in the numerical are mentioned in ratio A : B, then A : B will be AX and BX

2) If sum of ages of x and y is A and ratio of their ages is p : q respectively, then one can determine age of y by using the formula :

 Age of y = (Ratio of y/sum of ratio) × sum of ages

 Age of y =(q/(p + q))× A

Points to Remember:

- After reading the question, assume unknown age by some variable x.

- Convert the statements in the question into mathematical equations.

- Calculate the unknown by solving the equations and the obtained value must satisfy the conditions given in the problem.

Numerical on ages can be generally classified into four types:

Type1: Calculate Present age

Q 1. What is John’s present age, if after 10 years his age will be 5 times his age 5 years back.

a. 6.2 years

b. 7.7 years

c. 8.7 years

d. 10 years

Correct Option: (c)

Solution:

1) Let John’s present age be x

2) John’s age before 5 years = (x - 5)

3) John’s age after 10 years = (x + 10)

We are given that, John’s age after 10 years (x + 10) is 5 times his age 5 years back (x – 5)

Therefore,

(x + 10) = 5 (x – 5)

Solving the equation, we get

x + 10 = 5x – 25

4x = 35

x = 8.75 years

Q 2. Rahul is 15 years elder than Rohan. If 5 years ago, Rahul was 3 times as old as Rohan, then find Rahul's present age.

a. 32.5 years

b. 27.5 years

c. 25 years

d. 24.9 years

Correct Option: (b)

Solution:

1) Let age of Rohan be y

2) Rahul is 15 years elder than Rohan = (y + 15). So Rahul’s age 5 years ago = (y + 15 – 5)

3) Rohan’s age before 5 years = (y – 5) 5 years ago, Rahul is 3 times as old as Rohan

(y + 15 – 5) = 3 (y – 5) (y + 10) = (3y – 15)

2y = 25

y = 12.5

Rohan’s age = 12.5 years

Rahul’s age = (y + 15) = (12.5 + 15) = 27.5 years

Type 2: Numerical to Determine Ages in ratio form

Q 3. One year ago, ratio of Harry and Peter age’s was 5 : 6 respectively. After 4 years, this ratio becomes 6 : 7. How old is Peter?

a. 25 years

b. 26 years

c. 31 years

d. 35 years

Correct Option: (c)

Solution:

Hint: If ages in the numerical are mentioned in ratio A : B, then A : B will be Ax and Bx.

We are given that age ratio of Harry : Pitter = 5 : 6

1) Harry’s age = 5x and Peter’s age = 6x

2) One year ago, their age was 5x and 6x. Hence at present, Harry’s age = 5x +1 and Peter’s age = 6x +1

3) After 4 years,

Harry’s age = (5x +1) + 4 = (5x + 5)

Peter’s age = (6x +1) + 4 = (6x + 5)

4) After 4 years, this ratio becomes 6 : 7.

Therefore,

Harry’s Age/6 = Peter’s Age/7

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

7 (5x + 5) = 6 (6x + 5)

X = 5

Peter’s present age = (6x + 1) = (6 x 5 + 1) = 31 years

Harry’s present age = (5x + 1) = (5 x 5 + 1) = 26 years

Q 4. Age of mother 10 years ago was 3 times the age of her son. After 10 years, mother’s age will be twice that of his son. Find the ratio of their present ages.

a. 11 : 7

b. 9 : 5

c. 7 : 4

d. 7 : 3

Correct Option: (d)

Solution:

We are given that, age of mother 10 years ago was 3 times the age of her son.

So, let age of son be x and as mother’s age is 3 times the age of her son, let it be 3x, three years ago.

At present

Mother’s age will be (3x + 10) and son’s age will be (x + 10)

After 10 years

Mother’s age will be (3x + 10) +10 and son’s age will be (x + 10) + 10

Mother’s age is twice that of son

(3x + 10) +10 = 2 [(x + 10) + 10]

(3x + 20) = 2[x + 20]

Solving the equation, we get x = 20

We are asked to find the present ratio

(3x + 10) : (x + 10) = 70 : 30 = 7 : 3

Type 3: Numerical to Determine Age of a Person before x Years

Q 5. Sharad is 60 years old and Santosh is 80 years old. How many years ago was the ratio of their ages 4 : 6?

a. 10 years

b. 15 years

c. 20 years

d. 25 years

Correct Option: (c)

Solution:

Here, we have to calculate: How many years ago the ratio of their ages was 4 : 6

Let us assume x years ago

At present: Sharad is 60 years and Santosh is 80 years

x years ago: Sharad’s age = (60 – x) and Santosh’s age = (80 – x)

Ratio of their ages x years ago was 4 : 6

(60 – x)/(80 – x)=4/6

6(60 – x) = 4(80 – x)

360 – 6x = 320 – 4x

x = 20

Therefore, 20 years ago, the ratio of their ages was 4 : 6

Q 6. The ratio of Rohan’s age 4 years ago and Rahul’s age after 4 years is 1 : 1. If at present, the ratio of their ages is 5 : 3, then find the ratio between Rohan’s age 4 years hence and Rahul’s age 4 years ago.

a. 1 : 3

b. 3 : 1

c. 4 : 3

d. 3 : 4

Correct Option: (b)

Solution:

Hint: If ages in the numerical are mentioned in ratio A : B, then A : B will be Ax and Bx

1) At present: Ratio of their ages = 5 : 3.

Therefore, 5 : 3 will be 5x and 3x.

Rohan’s age 4 years ago = 5x – 4

Rahul’s age after 4 years = 3x + 4

2) Ratio of Rohan’s age 4 years ago and Rahul’s age after 4 years is 1 : 1

Therefore,

(5x – 4)/(3x + 4)=1/1

Solving, we get x = 4

3) We are asked to find the ratio between Rohan’s age 4 years hence and Rahul’s age 4 years ago.

Rohan’s age : (5x + 4)

Rahul’s age: (3x – 4)

Ratio of Rahul’s age and Rohan’s age

(5x + 4)/(3x – 4)=24/8=3/1

Type 4: Numericals to Determine Age of a Person after x Years

Q 7. 5 years ago, sister’s age was 5 times the age of her brother and the sum of present ages of sister and brother is 34 years. What will be the age of her brother after 6 years?

a. 12 years

b. 13.5 years

c. 15 years

d. 20 years

Correct Option : (c)

Solution:

We are given, 5 years ago sister’s age was 5 times the age of her brother.

Therefore,

(34 – x) – 5 = 5 (x – 5)

34 – x – 5 = 5x – 25

5x + x = 34 – 5 +25

6x = 54

x = 9

Future age (after 6 yrs) = (x + 6) = (9 + 6) = 15 years

Q 8. Father is 3 times more aged than his daughter. If after 5 years, he would be 3 times of daughter’s age, then further after 5 years, how many times he would be of his daughter’s age?

a. 1 (½) times

b. 2 times

c. 2.5 times

d. 3 times

Correct Option: (c)

Solution:

Let daughter’s age be x and father’s age be 3x.

Father’s age is 3 times more aged than his daughter, therefore father’s present age = x + 3x = 4x

After 5 years, father’s age is 3 times more than his daughter age.

(4x + 5) = 3 (x + 5)

x = 10

After 5 years it was (4x + 5), then after further 5 years, father’s age = (4x +10) and daughter’s age = (x + 10)

(4x + 10)/(x + 10)=?

Substitute the value of x, we get

[(4 × 10) + 10]/[10 + 10]=50/20=5/2=2.5

Free Mock Online Test for "Problems On Ages (Concepts & Related Solved Problems)":

https://gyangossip.com/problems-on-ages-part-1-/mock-test/T12809

https://gyangossip.com/problems-on-ages-part-2/mock-test/T12953

https://gyangossip.com/problems-on-ages-part-3-/mock-test/T13058