Problems on Ages

Father is four times the age of his daughter. If after 5 years, he would be threee times of daughter’s age, then further after 5 years, how many times he would be of his daughter’s age?

• 1.5 times

• 2 times

• 2.5 times

• 3 times

Answer explanation

Let father's age = x

Daughter's age = y

x = 4y

x + 5 = 3(y + 5).

4y+5 = 3y + 15

y = 10

Hence present age of daughter is 10 years and present age of father is 40 years.

So after 5 + 5 = 10 years, daughter age would be 20 years and father’s age would be 50 years.

Hence father would be 50/20 = 2.5 times of daughter’s age.

What is Aman's present age, if after 20 years his age will be 10 times his age 10 years back?

• 13.3

• 6.7

• 10

• 7.7

Answer explanation

Aman's present age be x

before 10 years = x - 10

after 20 years = (x + 20)

x + 20 = 10 (x – 10)

x + 20 = 10x – 100

9x = 120,

x = 13.3 years

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.

• 32.5

• 27.5

• 25

• 24.9

Answer explanation

Let

Age of Nisha be x

age of Romi be y

x = (y + 15).

5 years ago x - 5 = 3(y– 5).

(y + 15) – 5 = 3 (y – 5)

(y + 10) = (3y – 15)

2y = 25 ⇒ y = 12.5

Romi's age = 12.5 years

Nisha's age x = (y + 15) = (12.5 + 15) = 27.5

One year ago, the ratio of Honey and Piyush ages was 2: 3 respectively. After five years from now, this ratio becomes 4: 5. How old is Piyush now?

• 5

• 25

• 10

• 15

Answer explanation

Age ratio of H : P = 2: 3

H = 2x and P= 3x

One year ago, their age was 2x and 3x.

Now, H = 2x +1 and P = 3x +1

After 5 years, H = (2x +1) + 5 = (2x + 6)

P= (3x +1) + 5 = (3x + 6)

After 5 years, this ratio becomes 4: 5. Therefore,

(2x+6) / (3x+6) = 4/5

10x + 30 = 12x + 24

⇒ x = 3

P = (3x + 1) = (3x 3 + 1) = 10 years

Ten years ago, the age of mother was three times the age of her son. After ten years, mother’s age will be twice that of his son. Find the ratio of their present ages.

• 11:7

• 9:5

• 7:9

• 7:3

Answer explanation

At present age of Mother be x and

Son's age be y.

10 years ago, x-10 = 3(y-10)

x - 10 = 3y -30

x - 3y = -20 ....... (1)

After ten years, x+10 = 2 (y+10)

x+10 = 2y +20

x - 2y = 10........ (2)

Solving the equation 1 & 2

, we get y = 30

and x = 70

x:y = 70: 30 = 7: 3.

Saransh is 50 years old and Nazma is 40 years old. How long ago was the ratio of their ages 3:2?

• 20

• 30

• 40

• 25

Answer explanation

x years ago: S = (50 – x) and N= (40 – x)

Given, the ratio of their ages was 3:2

(50-x) / (40-x) = 3/2

Solving, we get: x = 20

Therefore, the answer is 20 years.

The ratio of the present ages of Pranav and Qureshi is 4:5. Five years ago, the ratio of their ages was 7:9. Find their present ages?

• 18,25

• 40,50

• 25,35

• 20,30

Answer explanation

Their present ages be 4X and 5X.

5 years ago, the ratio of their ages was 7:9, then (4X - 5) /( 5X - 5) = 7/9

X = 45 - 35 ⇒ X = 10.

Their present ages are: 40, 50.