1. 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?

Sol : Option C
Let the daughter's age be x and father's age be 4x.
So as per question, 4x + 5 = 3(x + 5). So x = 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.

Q.2. What is Aman's present age, if after 20 years his age will be 10 times his age 10 years back?

A. 6.2 years

B. 7.7 years

C. 13.3 years

D. 10 years

Sol : Option C
Let Aman's present age be x
Aman's age before 10 years = x - 10)
Aman's age after 20 years = (x + 20)
We are given that, Aman's age after 20 years (x + 20) is 10 times his age 10 years back (x – 10)
Therefore, (x + 20) = 10 (x – 10)
Solving the equation, we get x + 20 = 10x – 100
9x = 120, x = 13.3 years

Q.3. 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.

A. 32.5 years

B. 27.5 years

C. 25 years

D. 24.9 years

Sol : Option B
Let age of Romi be y
Nisha is 15 years elder than Romi = (y + 15). So Nisha's age 5 years ago = (y + 15 – 5).
Romi's age before 5 years = (y – 5)
5 years ago, Nisha is 3 times as old as Romi
(y + 15 – 5) = 3 (y – 5)
(y + 10) = (3y – 15)
2y = 25 ⇒ y = 12.5
Romi's age = 12.5 years
Nisha's age = (y + 15) = (12.5 + 15) = 27.5 years.

Q.4. 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?

A. 5 years

B. 25 years

C. 10 years

D. 15 years

Sol : Option C
We are given that age ratio of Honey: Piyush = 2: 3
Honey’s age = 2x and Piyush’s age = 3x
One year ago, their age was 2x and 3x.
Hence at present, Honey's age = 2x +1 and Piyush's age = 3x +1
After 5 years, Honey’s age = (2x +1) + 5 = (2x + 6)
Piyush's age = (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
Piyush's present age = (3x + 1) = (3x 3 + 1) = 10 years
Honey's present age = (2x + 1) = (2x 3 + 1) = 7 years

Q.5. 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.

A. 11 : 7

B. 9 : 5

C. 7 : 4

D. 7 : 3

Sol : Option D
10 years ago, age of mother was three times the age of her son. Say, the age of son was x and mother's age was 3x.
At present: Mother's age is (3x + 10) and son’s age is (x + 10)
After ten years: Mother's age will be (3x + 10) +10 and son’s age will be (x + 10) + 10. Given that, mother’s age is twice that of son after ten years.
(3x + 10) +10 = 2 [(x + 10) + 10]
(3x + 20) = 2[x + 20]
Solving the equation, we get x = 20
(3x + 10): (x + 10) = 70: 30 = 7: 3.

Q.6. Saransh is 50 years old and Nazma is 40 years old. How long ago was the ratio of their ages 3:2?

A. 20 years

B. 30 years

C. 40 years

D. 25 years

Sol : Option A
Here, we have to calculate: How many years ago the ratio of their ages was 3:2. Let us assume x years ago
At present: Saransh is 50 years and Nazma is 40 years
x years ago: Saransh’s age = (50 – x) and Nazma's age = (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.

Q.7. 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? (In years)

A. 40, 50

B. 18, 25

C. 40, 60

D. 20, 25

Sol : Option A
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.

Q8. A man said to his son, "I was one-third of your present age when you were born". If the present age of the man is 48 years, find the present age of the son.

Sol : Option D
Present age of the son be P, he was born P years ago.
The age of the man was: (48 - P).
His age when the son was born should be equal to 1/3 of P.
(48 - P) =1/3 P ⇒ P = 36

Q9. Dinesh is younger to Roshan by 9 years. If their ages are in the respective ratio of 4:5, how old is Dinesh?

A. 36 years

B. 23years

C. 29 years

D. Cannot be determined

Sol : Option A
Let Roshan's age be x years.
Then, Dinesh 's age = (x - 9) years.
(x - 9)/x = 4/5
x = 45 Hence, Dinesh's age = (x - 9) = 36 years.

Q10. The ratio of Sara’s age 4 years ago and Vaishali’s age after 4 years is 1: 1. Presently, the ratio of their ages is 5: 3. Find the ratio between Sara’s age 4 years hence and Vaishali’s age 4 years ago.

A. 1 : 3

B. 3 : 1

C. 4 : 3

D. 3 : 4

Sol : Option B
Currently, the ratio of their ages is 5: 3. Suppose, their ages are: 5x and 3x.
Sara’s age 4 years ago = 5x – 4
Vaishali’s age after 4 years = 3x + 4
Ratio of Sara’s age 4 years ago and Vaishali's age after 4 years is 1 : 1
Therefore,
(5x - 4) / (3x + 4) = 1/1
Solving, we get x = 4
We are required to find the ratio between Sara’s age 4 years hence and Vaishali’s age 4 years ago.
Sara's age: (5x + 4)
Vaishali's age: (3x – 4)
Putting the value of x, we get:
(5x + 4) / (3x - 4) = 3/1 = 3:1