BANK & INSURANCE (AGE BASED PROBLEMS) PART 2

Total Questions: 45

21. There were 15 students in a class. When the ages of a teacher and a new boy are added, the average age of the class increases by 10 per cent while it remains the same when only the age of a boy is added. If the teacher's age is eight years more than twice the age of the new boy, then find the initial average age of the class.

Correct Answer: (a) 11.4 years
Solution:

Let average age of 15 students be x

15x + T + B = 1.10x × 17

T + B = 3.7x ...(i)

Also, 15x + B = 16x Or, B = x ...(ii)

And, T = 8 + 2B

3.7x = 8 + 2x + 0r,

x = 11.4 years

22. The ratio of present age of Ankur to present age of Sanjeev is 3 : 11 while the ratio of present age of Sanjeev to present age of Reena is 5 : 4. If the average age after 7 years of all three of them will be 45 years, then find the present age of Reena.

Correct Answer: (d) 44 years
Solution:

Ratio of present ages of Ankur and Sanjeev = 3 : 11

Ratio of present ages of Sanjeev and Reena = 5 : 4

Equating the ratios, we get Ratio of present ages of
Ankur, Sanjeev and Reena = 15 : 55 : 44

Let Ankur's age be 15x, Sanjeev's age be 55x and Reena's age be 44x

Using the data provided in the question, we get

15x + 55x + 44x + 21 = 45 × 3

114x = 114

x = 1

Reena's present age = 44x = 44 years

23. At the time of marriage, the ratio of ages of the husband and his wife was 6:7, respectively. 6 years hence from marriage, the husband's age was 50% more than it was 4 years before marriage. What was the age of wife at the time of marriage?

Correct Answer: (a) 28 years
Solution:

Let the age of the husband at the time of marriage = '6y' years

Then, age of the wife at the time of marriage = '7y' years

According to the question,

(6y + 6) = (6y − 4) × 1.50

Or,

6y + 6 = 9y − 6

Or,

y = 4

So, age of wife at the time of marriage

= 7 × 4 = 28 years

24. Present age of 'A' is 37.5% more than that of 'B'. If eight years hence from now, their average age will be 11 years more than present age of 'B', then find the present age of 'B'.

Correct Answer: (e) 16 years
Solution:

Let the present age of 'B' be '8x' years

So, present age of 'A' = 8x × 1.375 = 11x years

ATQ,

((11x + 8x) + 8 + 8)/2 = 8x + 11

19x + 16 = 16x + 22

3x = 6

So, x = 2

So, present age of 'B' = 2 × 8 = 16 years

25. Present age of the mother is 6 times the present age of his son. The present age of the father is 7 years more than 5 times the present age of the son. If the sum of present ages of the mother and the father is 62 years, then find the ratio of age of son, 40 years hence from now to the age of mother 12 years ago from now.

Correct Answer: (a) 5:2
Solution:

Let the present age of the son be 'x' years

Therefore, present age of the mother

= 6 × x = 6x years

Present age of the father = (5x + 7) years

According to the question,

5x + 7 + 6x = 62

11x = 55

x = 5

Therefore, present age of the son = x = 5 years

Present age of Mother = 6 × 5 = 30 years

Required ratio = (5 + 40) : (30 − 12)

= 45 : 18 = 5 : 2

26. 2 years ago from now, the age of Arjun was 20% less than that of Bheem. 2 years hence from now, the age of Bheem will be 20% more than that of Arjun. Find the sum of present ages of Bheem and Arjun.

Correct Answer: (e) 40 years
Solution:

2 years ago from now, let the age of Bheem = 10y years

Then, 2 years ago from now, age of Arjun = 10y × 0.8

= 8y years

2 years hence from now, age of Bheem = 10y + 2 + 2

= (10y + 4) years

2 years hence from now, age of Arjun = 8y + 2 + 2

= (8y + 4) years

According to the question,

10y + 4 = (8y + 4) × 1.2

10y + 4 = 9.6y + 4.8

0.4y = 0.8

So, y = 2

So, present ages of Bheem and Arjun are (10y + 2) and (8y + 2)

i.e. 22 and 18 years, respectively.

So, required sum = 22 + 18 = 40 years

27. The sum of present ages of 'A', 'B', 'C' and 'D' is 94 years, where the present age of 'C' is 60% of the present age of 'D' and 50% more than the present age of 'A'. 6 years hence from now, if the age of 'B' will be 25% more than his present age, then find the average present age of 'C' and 'D'.

Correct Answer: (d) 28 years
Solution:

Let the present age of 'A' = 2y years

Then, present age of 'C' = 2y × 1.5 = 3y years

Present age of 'D' = 3y ÷ 0.6 = 5y years

Let the present age of 'B' = x years

According to the question,

(x + 6) = x × 1.25

0.25x = 6

So, x = 6 ÷ 0.25 = 24

And so, sum of present ages of 'A', 'C' and 'D'

= 2y + 3y + 5y = 10y years

So, 10y = 94 − 24 = 70

So, y = (70/10) = 7

So, average of present age of 'C' and 'D'

= (3y + 5y) ÷ 2 = 4y = 28 years

28. Eight years ago from now, the average age of a family of 4 members was 20 years. If 3 years ago, a baby was born in the family, then find the present average age of the family given that no one else died or was born during given period.

Correct Answer: (b) 23 years
Solution:

Total age of the family 8 years ago from now = 4 × 20 = 80 years

Total age of the family now

= 80 + (4 × 8) + 3

= 115 years

So, average present age of the family

= 115 ÷ 5 = 23 years

29. Six years hence from now, the ratio of ages of Ram and Shyam will be 16:19, respectively. Find the ratio of their present ages given that the numerical value of the product of their ages, six years hence from now, will be 2736.

Correct Answer: (a) 14:17
Solution:

6 years hence from now, let the ages of Ram and Shyam will be '16x' years and '19x' years, respectively.

Given, 16x × 19x = 2736

304x² = 2736

x² = 9

x = ±3

x = 3 [Since, age cannot be negative]

Age of Ram, six years hence from now = 16x = 16 × 3 = 48 years

Age of Shyam, six years hence from now = 19x = 19 × 3 = 57 years

Present age of Ram = 48 − 6 = 42 years

Present age of Shyam = 57 − 6 = 51 years

Ratio of present ages of Ram and Shyam = 42 : 51

= 14 : 17

30. 4 years ago from now, the ratio of ages of Kalai and Maran was 5:6 respectively. 4 years hence from now, the ratio of ages of Maran and Kalai will be 7:6 respectively. Find the difference between the ages of Kalai and Maran.

Correct Answer: (e) 8 years
Solution:

4 years hence from now,

Let the age of Maran = 7x years

Then, age of Kalai = 6x years

4 years ago from now,

Age of Maran = 7x − 4 − 4 = (7x − 8) years

Age of Kalai = (6x − 8) years

According to the question,

(6x − 8) : (7x − 8) = 5 : 6

36x − 48 = 35x − 40

x = 8

So, difference between the ages of Kalai and Maran = 6x − 5x = x = 8 years