0

Problem of Ages - II

Description: BANK SSC QUANT
Number of Questions: 15
Created by:
Tags: BANK SSC QUANT Word Problems on Linear Equations Arithmetic Quantitative Aptitude
Attempted 0/15 Correct 0 Score 0

The ratio between the present ages of P and Q is 3 : 7. If after 5 years, the age of Q becomes twice the age of P, then find the present age of P.

  1. 15 years

  2. 12 years

  3. 21 years

  4. 18 years

  5. 24 years


Correct Option: A
Explanation:

Let the present age of P be 3x years.

So the present age of Q be 7x years.

Now, after 5 years, P's age = 3x + 5 years and Q's age = 7x + 5 years

So, according to question,

2(3x + 5) = 7x + 5

On solving this equation, we get

x = 5

So, the present age of P is 3x = 3 * 5 = 15 years.

Ram's age, four years ago, was 7/8 of Laksham's age. If Ram's present age is 32 years, what is Laksham's present age?

  1. 30 years

  2. 24 years

  3. 36 years

  4. 40 years

  5. 32 years


Correct Option: C
Explanation:

Ram's present age = 32 years

Four years ago, Ram's age = 32 - 4 = 28 years

Four years ago, Laksham's age = 28 * 8/7 = 32 years

Now, present age of Laksham = 32 + 4 = 36 years

Amit's age, 5 years hence, will be 8/5 times his age 7 years back. What is the present age of Amit?

  1. 27 years

  2. 23 years

  3. 20 years

  4. 25 years

  5. 28 years


Correct Option: A
Explanation:

Let the present age of Amit be x years.

5 years hence, Amit's age = x + 5 years 

7 years back, Amit's age = x - 7 years 

Now, according to question,

x + 5 = 8/5(x - 7)

x = 27

So, the present age of Amit is 27 years.

Ten years ago, Rekha's age was 10 years more than twice of Megha's age. Six years hence, sum of their ages will be 78 years. Find the ratio of their present ages.

  1. 21 : 12

  2. 2 : 1

  3. 1 : 2

  4. 31 : 35

  5. 25 : 41


Correct Option: B
Explanation:

Ten years ago, let Megha's age be x years. 

Then, Rekha's age = 2x + 10 years 

So, present age of Rekha = 2x + 10 + 10 = 2x + 20 years and present age of Megha = x + 10 years 

Now, six years hence, Rekha's age = 2x + 20 + 6 = 2x + 26 years and Megha's age = x + 10 + 6 = x + 16 years 

According to question,

2x + 26 + x + 16 = 78

x = 12

So, ten years ago, Megha's age = 12 years and Rekha's age = 2 x 12 + 10 = 34 years 

Now, present age of Rekha = 34 + 10 = 44 years and pressent age of Megha = 12 + 10 = 22 years

So, ratio of their present ages = 44 : 22 = 2 : 1

Akash is 30 years younger than his father. Four years ago, Akash was 2/5th as old as his father. How old will Akash's father be 6 years from today?

  1. 50 years

  2. 54 years

  3. 40 years

  4. 60 years

  5. 64 years


Correct Option: D
Explanation:

Let the present age of father be x years.

Then, present age of Akash = x - 30 years 

Four years ago, Akash's father's age = x - 4 years and Akash's age = x - 30 - 4 = x - 34 years

According to the question,

x - 34 = 2/5(x - 4)

x = 54

Akash's father's present age = 54 years 

So, father's age after 6 years = 54 + 6 = 60 years

The ages of A and B are in the ratio 4 : 5. After 14 years, the ratio of their ages will be 6 : 7. What was the difference of their ages 5 years ago?

  1. 5 years

  2. 7 years

  3. 6 years

  4. 4 years

  5. 8 years


Correct Option: B
Explanation:

Let the present age A be 4x years and that of B be 5x years. 

After 14 years, A's age = 4x + 14 years and B's age = 5x + 14 years

Now, according to question, 

(4x + 14)/(5x + 14) = 6/7

x = 7

Now, present age of A = 4 * 7 = 28 years and present age of B = 5 * 7 = 35 years

Age of A 5 years ago = 28 - 5 = 23 and B's age 5 years ago = 35 - 5 = 30 years

So, the difference of ages of A and B is 30 - 23 = 7 years.

A father is 14 times older than his son. After 12 years, his age will be 20/7 of the age of his son. Find the present age of the father.

  1. 30 years

  2. 32 years

  3. 26 years

  4. 28 years

  5. 24 years


Correct Option: D
Explanation:

Let the present age of son be x years.

Then, present age of father = 14x years

After 12 years, son's age = x + 12 years and father's age = 14x + 12 years 

Now, according to question,

20/7(x + 12) = 14x + 12

x = 2

So, present age of father = 14x = 14 * 2 = 28 years

The sum of the present ages of both father and son is 86 years. Five years ago, the father was 2 years less than twice as old as his son at that time. Find the present age of the son.

  1. 31 years

  2. 30 years

  3. 32 years

  4. 34 years

  5. 36 years


Correct Option: A
Explanation:

Let the present age of father be x years and that of the son 86 - x years.

Five years ago, father's age = x - 5 years and son's age = (86 - x - 5) = 81 - x years

Now, according to question,

x - 5 = 2(81 - x) - 2

x = 55

So, present age of father = 55 years 

Therefore, present age of son = 86 - 55 = 31 years

If a son is younger than his father by 23 years and 5 years ago, the father was 30 years old, then what is the sum of their ages after 10 years?

  1. 70 years

  2. 80 years

  3. 72 years

  4. 67 years

  5. 52 years


Correct Option: D
Explanation:

Let the present age of father be x years.

Five years ago, father's age = x - 5 years

Now, according to question,

x - 5 = 30

x = 35 years

So, father's present age = 35 years

So, son's present age = 35 - 23 = 12 years 

Now, total age of father and son after 10 years = (35 + 10) + (12 + 10) = 67 years

The age of father is 2 years more than twice his son's present age. After 7 years, the sum of their ages will be 121 years. Find the present age of the father.

  1. 70 years

  2. 76 years

  3. 72 years

  4. 60 years

  5. 66 years


Correct Option: C
Explanation:

Let the present age of the son be x years.

Then, present age of father = 2x + 2 years 

Now, after 7 years, son's age = x + 7 years and father's age = 2x + 2 + 7 = 2x + 9 years

Now, according to question, 

x + 7 + 2x + 9 = 121 

x = 35

So, present age of son = 35 years

Therefore, present age of father = 35 * 2 + 2 = 72 years

Anuj is 2 years younger than Rakesh and Rakesh is 39 years younger than Rahul. If the age of Rahul is 3 times of the sum of ages of Anuj and Rakesh, then find the present age of Rahul.

  1. 48 years

  2. 46 years

  3. 40 years

  4. 50 years

  5. 44 years


Correct Option: A
Explanation:

Let the present age of Rahul be x years.

Then, present age of Rakesh = x - 39 years 

So, present age of Anuj = x - 39 - 2 = x - 41 

Now, according to question,

x = 3(x - 39 + x - 41)

x = 48 years

Present ages of Mohit and Lalit are 32 and 56 years, respectively. How many years ago was the ratio of their ages 1 : 2?

  1. 10 years

  2. 8 years

  3. 6 years

  4. 12 years

  5. 5 years


Correct Option: B
Explanation:

Let x years ago, the ratio of the ages of Mohit and Lalit be 1 : 2.

So, (32 - x)/(56 - x) = 1/2

x = 8 years

The sum of the ages of a father and his son is 40 years. Four years ago, the father's age was 3 times his son's age. What is the present age of the father?

  1. 28 years

  2. 32 years

  3. 30 years

  4. 25 years

  5. 20 years


Correct Option: A
Explanation:

Let the present age of father be x years. So, present age of son = 40 - x years Four years ago, age of father = x - 4 years and age of son = 40 - x - 4 = 36 - x years Now, according to question, x - 4 = 3(36 - x) On solving this equation, we get x = 28 years So, the present age of father is 28 years.

A is 5 years older than B, who is 2 years older than half of age of C. If the average age of A, B and C is 59 years, then find the age of B after 6 years.

  1. 50 years

  2. 44 years

  3. 60 years

  4. 54 years

  5. 40 years


Correct Option: A
Explanation:

Let the present age of A be x years.

Then, present age of B = x - 5 years and that of C = 2(x - 5 - 2) = 2x - 14 years 

So, average of A, B and C = 59 years 

(x + x - 5 + 2x - 14)/3 = 59

x = 49

So, the present age of A is 49 years.

Then present age of B = 49 - 5 => 44 years 

Therefore B's age after 6 years = 44 + 6 => 50 years.

The age of a father, 9 years ago, was 4 times the age of his son. Nine years hence, the age of the father will be twice that of his son. Find the present age of the father.

  1. 40 years

  2. 42 years

  3. 47 years

  4. 45 years

  5. 50 years


Correct Option: D
Explanation:

Let the present age of father be x years and that of the son be y years.

Then, 9 years ago, father's age = x - 9 and son's age = y - 9 years

So, according to question,

x - 9 = 4 (y - 9) 

x - 4y = -27 ------------------(1)

Now, 9 years hence, father's age = x + 9 years and son's age = y + 9 years

Again, x + 9 = 2(y + 9)

x - 2y = 9 -------------------------(2)

On solving the equations (1) and (2), we get

x = 45 and y = 18

So, the present age of father is 45 years.

- Hide questions