BANK & INSURANCE (AGE BASED PROBLEMS) PART 3

Let the present ages of ‘A’ and ‘B’ be 9x years and 5x years respectively.

Four years ago, Age of ‘C’ = 0.75 × 9x = 6.75x years

Therefore, present ages of ‘C’ = (6.75x + 4) years

Therefore, present age of ‘D’ = {(9x + 5x + 6.75x + 4)/3}
= (20.75x + 4)/3 years

According to the question,

[(5x + 5) / {((20.75x + 4)/3) + 16}] = 5/9

27(x + 1) = 20.75x + 4 + 48

6.25x = 25

x = 4

Required difference = 9x − (6.75x + 4)

= 2.25x − 4

= 5 years

Let the present age of ‘B’ be ‘2x’ years

So, present age of ‘C’ = 2x × 1.4 = 2.8x years

And, present age of ‘A’ = 2.8x ÷ 2 = 1.4x years

ATQ:

(2.8x + 1.4x)/2 = 2x + 1.5

4.2x = 4x + 3

0.2x = 3

So,

x = 15

Required average = (1.4x + 2x + 2.8x) ÷ 3

= 6.2x ÷ 3

= (6.2 × 15) ÷ 3

= 31 years

Let the present age of ‘B’ = 10x years

Then, average of the present ages of ‘A’ and ‘C’

= 10x × 0.6 = 6x years

Sum of present ages of ‘A’ and ‘C’

= 2 × 6x = 12x years

Present age of ‘D’ = 6x × 1.50 = 9x years

According to the question,

((10x + 2) / (9x − 3)) = 4/3

30x + 6 = 36x − 12

6x = 18

x = 3

So, average of the present ages of ‘A’, ‘B’ and ‘C’ = (10x + 12) ÷ 3

= (22x/3)

= (22/3) × 3

= 22 years

Let the present age of ‘B’ = 20x years

So, present age of ‘A’ = x × 1.25 = 25x years

Average age of ‘A’ over the last 4 years

= (25x + (25x − 1) + (25x − 2) + (25x − 3)) ÷ 4

= (100x − 6)/4 years

Average age of ‘B’ over the last 4 years

= (20x + (20x − 1) + (20x − 2) + (20x − 3)) ÷ 4

= (80x − 6)/4 years

ATQ:

((100x − 6)/4) × 15 = 19 × ((80x − 6)/4)

60x = 72

So,

x = 1.2

So, present age of ‘A’ = 1.2 × 25 = 30 years

Let the present age of ‘B’ be ‘6x’ years

So, present age of ‘A’ = 6x × (5/3) = ‘10x’ years

And, present age of ‘C’ = 6x × (7/6) = ‘7x’ years

ATQ:

10x − 7x ≥ 16

3x ≥ 16

The minimum integral value of ‘x’ that satisfies the given inequality is 6

So, minimum possible present age of ‘B’

= 6 × 6 = 36 years

Let the present ages of ‘A’ and ‘B’ be ‘5x’ years and ‘6x’ years respectively.

For statement I:

(5x − 5) × 1.25 = (6x − 5)

6.25x − 6.25 = 6x − 5

0.25x = 1.25

So,

x = 5

So, sum of present ages of ‘A’ and ‘B’

= 6x + 5x = 11x

= 11 × 5 = 55

So, sum of ages of ‘A’ and ‘B’ after 12 years from now

= 55 + 12 + 12 = 79 years

Therefore, statement I is true.

For statement II:

(5x − 5) × 1.20 = (6x − 5)

6x − 6 = 6x − 5

−6 = −5 (not possible)

Therefore, statement II is false.

For statement III:

(5x − 5) × 1.40 = (6x − 5)

7x − 7 = 6x − 5

x = 2

So, sum of present ages of ‘A’ and ‘B’

= 6x + 5x = 11x

= 11 × 2 = 22 years

So, sum after ages of ‘A’ and ‘B’ after 12 years from now

= 22 + 12 + 12

= 46 years

Therefore, statement III is true.

Let present ages of ‘A’, ‘B’ and ‘C’ be ‘a’ years, ‘b’ years and ‘c’ years respectively.

So,

(a + 12) = 5 + 1.5 × (b − 18)

a + 12 = 5 + 1.5b − 27

1.5b − a = 34  …(1)

Also,

c = a + 4

And,

(c + 25) = 1.75 × ((a + b)/2)

2c + 50 = 1.75a + 1.75b

2a + 8 + 50 = 1.75a + 1.75b

1.75b − 0.25a = 58  …(2)

Multiplying equation (1) by 0.25 and subtracting it from equation (2), we get

1.75b − 0.375b = 58 − 0.25 × 34

1.375b = 49.5

b = 36

So,

a = 1.5b − 34

= 1.5 × 36 − 34

= 20

So, present age of ‘C’

= 20 + 4

= 24 years

2 years ago from now, let the age of Varsha’s brother be ‘5x’ years

Present age of Varsha’s brother

= (5x + 2) years

8 years hence from now, age of Varsha's brother
= (5x + 2 + 8) = (5x + 10) years

5 years ago from now, age of Varsha's mother
= (7/5) × (5x + 10) = (7x + 14) years

Therefore, present age of Varsha's mother
= 7x + 14 + 5 = (7x + 19) years

Therefore, 2 years hence from now, age of Varsha
= 1.8 × 5x = 9x years

Present age of Varsha = (9x − 2) years

According to the question,

9x − 2 + 5x + 2 + 7x + 19 = 61

21x = 42

x = 2

Therefore, present age of Varsha
= 9x − 2 = 9 × 2 − 2 = 16 years

Let the present age of Ram = ‘x’ years

Let the present age of Karim = ‘y’ years

According to the question,

(x − 4) : (y + 1) = 5 : 7

7x − 28 = 5y + 5

5y = 7x − 33 .......... (i)

Also,

(x + 6) : (y − 12) = 5 : 4

4x + 24 = 5y − 60

5y = 4x + 84 .......... (ii)

From equation (i) and (ii), we have

7x − 33 = 4x + 84

3x = 117

So,

x = (117/3) = 39

So, present age of Karim

y = (39 × 7 − 33) ÷ 5

= 48 years

So, difference between present ages of Karim and Ram

= 48 − 39 = 9 years

So, age of Karim when he was twice as old as Ram

= 9 × 2 = 18 years

Therefore, 48 − 18 = 30 years ago, Karim was twice as old as Ram.

Let Rita's present age = x years

Rita's daughter age = x/4 years

Rita's mother age = 3x/2 years

x + x/4 + 3x/2 = 154

(4x + x + 6x)/4 = 154

11x/4 = 154

⇒ x = 56

Rita's mother age = (3/2) × 56

= 3 × 28

= 84 years

Difference between Rita's age and her mother's age

= 84 − 56 = 28 years