BANK & INSURANCE (AGE BASED PROBLEMS) PART 2

Total Questions: 45

11. If the ages of P and Q are added to twice the age of R, the total becomes 61 if the ages of Q and R are added to thrice age of P, the total becomes 45 and if the age of P is added to thrice the age of Q and twice the age of R, the total becomes 89. What is the age of P?

Correct Answer: (b) 3 years
Solution:

Let ages of P, Q and R be a, b and c years respectively.

According to the given information:

a + b + 2c = 61 ...(i)

3a + b + c = 45 ...(ii)

a + 3b + 2c = 89 ...(iii)

Solving these three equations simultaneously, we get:

a = 3, b = 14, c = 22

Hence the age of P = a = 3 years

12. The average age of a father, a mother and a son 6 years ago was 30 years. By including a daughter present age the present average age of all four members of a family is 29. At present the average age of a father and a mother is 46 years. Find the difference between present age of a son and present age of a daughter.

Correct Answer: (c) 8 years
Solution:

Average = (sum of elements)/(number of elements)

Given,

The average age of a father, a mother and a son 6 years ago was 30 years

Then, the average age of a father, a mother and a son at present = 30 + 6 = 36 years

At present, Total sum of ages of a father, a mother and a son = 36 × 3 = 108 years

The present average age of all four members of a family = 29 years

At present, Total sum of ages of all four members of a family
= 29 × 4 = 116 years

Daughter's present age = 116 − 108 = 8 years

Given,

At present,
The average age of a father and a mother is 46 years

Total sum of ages of a father and a mother
= 46 × 2 = 92 years

Total sum of ages of a son and a daughter
= 116 − 92 = 24

The present age of a son = 24 − 8 = 16 years

The difference between the present ages of a son and a daughter = 8 years

= 16 − 8
= 8 years

∴ The difference between the present ages of a son and a daughter is 8 years.

13. Ratio of present age of P and Q is 4 : 5. Sum of the present age of S and P is 47. R is 2 year younger than Q. Average of present age of Q, R and S is 25. Find the difference between S and Q's age.

Correct Answer: (b) 2
Solution:

Let, age of P = 4x and age of Q = 5x

According to problem,

Age of S = 47 − 4x

Age of R = 5x − 2

According to problem,

⇒ 1/3 (5x + 5x − 2 + 47 − 4x) = 25

⇒ 6x + 45 = 75

⇒ 6x = 30

⇒ x = 5

Difference between ages of S and Q

⇒ 47 − 4x − 5x

⇒ 47 − 9x

⇒ 47 − 45

⇒ 2 years

14. A couple with average age 25 years bought a house. Three more members from the male's family came to live with them. Thus the average age of family got increased by 40%. If in the members who joined later only one is male with age 45 years. Find sum of the age of males is what percent of sum of ages of female members, if the ratio of ages of male to female earlier is 3 : 2.

Correct Answer: (b) 75%
Solution:

Average age of members in the family = 25

Total age = 2 × 25 (couple only)

= 50 years

According to the question,

3x + 2x = 50

⇒ x = 10

Age of male = 30 and Female = 20 years

After entry of 3 more members

New average = 25 × 140/100

= 35 years

Total age of 5 members = 35 × 5 = 175 years

Age of New members = 175 − 50 = 125 years

According to the question,

Age of new man included is 45 years, hence the age of new female member = 80 years

Sum of ages of men = 30 + 45 = 75 years

Required percentage,

Sum of ages of women = 20 + 80 = 100 years

75 + 100 × y/100

y = 75%

15. Rajesh got married 7 years ago. His present age is 8/7 times of his age at the time of marriage. At the time of his marriage, his brother was 5 years younger to him. What will be the age of his brother after 10 years?

Correct Answer: (d) 61 years
Solution:

x = (8/7) × (x − 7)

⇒ x = 56 years

So at the time of marriage his brother's age = (x − 7) − 5

= 44 years

Present age of his brother = 44 + 7 = 51 years

∴ Age of his brother after 10 years = 61 years.

16. The ratio between the twice of present age of P and present age of Q is 5 : 1. After 4 years, the ratio between the age of P and Q will be 2 : 1. Find the average age of P and Q after 4 years.

Correct Answer: (a) 18 years
Solution:

Let present age of P and Q be M and N years respectively.

Given,

⇒ 2M : N = 5 : 1

⇒ M = 5N/2

⇒ (M + 4) : (N + 4) = 2 : 1

⇒ M + 4 = 2N + 8

⇒ M − 2N = 4

⇒ 5N/2 − 2N = 4

⇒ N = 8 years

M = 20 years

Required average

= [(8 + 4) + (20 + 4)] / 2

= 18 years

17. Three years from now the age of Abhay will be 62.5% of his father's age. If the sum of their present age is 98 years then find the present age of Abhay.

Correct Answer: (a) 37 years
Solution:

Let the present age of Abhay and his father be x and y respectively.

So x + y = 98 ...(i)

3 years from now,

(x + 3) = 62.5% of (y + 3)

⇒ (x + 3) = (5/8)(y + 3)

⇒ 8x + 24 = 5y + 15

⇒ 8x − 5y = −9 ...(ii)

Multiplying 5 in equation 1 we get

5x + 5y = 490 ...(iii)

Adding equation (ii) and (iii) we get

13x = 481

⇒ x = 37

∴ The age of Abhay is 37 years

18. The ratio between the present age of Manav and Manoj is 2 : 3 respectively. The ratio of present age of Manav and Shyam is 4 : 5. If the average of the present age of them is 20 years, then find the present age of each person.

Correct Answer: (a) 16, 24, 20
Solution:

Manav : Manoj = 2 : 3 ...(i)

Manav : Shyam = 4 : 5 ...(ii)

So, Manav ratio must be similar in both equation because age is same in every condition

Now equation (i) multiply by 2

⇒ Manav : Manoj = 4 : 6

Ratio of three together

Manav : Manoj : Shyam = 4 : 6 : 5

Let the present ages of Manav, Manoj and Shyam be 4x, 6x and 5x respectively

Average = sum of observation / number of observation

⇒ 20 = (4x + 6x + 5x) / 3

⇒ 60 = 15x

⇒ x = 4

So,

4x = 4 × 4 = 16

5x = 6 × 4 = 24

6x = 5 × 4 = 20

∴ Age of Manav, Manoj and Shyam are 16, 24, 20 years respectively

19. Rahul's present age is 2 times his daughter's present age and two-third of his mother's present age. The average age of all of them is 32 years. What is the difference between Rahul's daughter present age and Rahul's mother's present age.

Correct Answer: (d) 32 years
Solution:

Let Rahul's age be x, his daughter's age be y and his mother's age be z

A.T.Q

x = 2y

y = x/2 ...(i)

z = 3x/2 ...(ii)

Average age = 32 years

(x + y + z) / 3 = 32

x + y + z = 32 × 3

On putting the value of eq. (i) and (ii), we get

x + x/2 + 3x/2 = 96

6x = 96 × 2

⇒ x = 32 years

Rahul's age = 32 years

Daughter's age = 16 years

Mother's age = 48 years

Required difference = 48 − 16 = 32 years

20. Respective ratio between A's age seven years hence and B's age nine years hence will be 5 : 6. If B is seven years older than A, what is B's present age? (In years)

Correct Answer: (d) 45
Solution:

Let A's present age = x years

B's present age = (x + 7) years

According to the question,

(x + 7)/(x + 16) = 5/6

⇒ 6x + 42 = 5x + 80

⇒ x = 38

B's present age = 38 + 7 = 45 years