BANK & INSURANCE (AGE BASED PROBLEMS) PART 2

Total Questions: 45

1. The ratio of the ages of Mary to that of her brother at present is 8 : 7 and the ratio of ages of Mary's brother to that of their mother 5 : 9. If the difference between the ages of Mary and her mother is 23, what is the age of Mary's mother?

Correct Answer: (a) 63 years
Solution:

The ratio of the ages of Mary to that of her brother at present is 8 : 7 and the ratio of Mary's brother to that of their mother 5 : 9

Formula:
If ratio of A and B is = x : y
∴ A / B = x / y

Calculation:

Ratio of the ages of Mary to that of her brother = 8 : 7
= (8 × 5) : (7 × 5) = 40 : 35

Ratio of ages of Mary's brother to that of their mother = 5 : 9
= (5 × 7) : (9 × 7) = 35 : 63

∴ Ratio of ages of Mary and her mother = 40 : 63

Let, age of Mary = 40x
∴ Age of Mary's mother = 63x

According to the question,

⇒ 63x − 40x = 23

⇒ 23x = 23

⇒ x = 1

∴ Age of Mary's mother = 63 × 1 = 63 years

2. The present ages of P and Q are in the ratio 3 : 4 respectively. The average of present ages of P,Q, R and S is 28 years. The ages of R and Q, 4 years hence would be in the ratio of 5 : 4 respectively. S's present age is ____ and he is 8 years elder to R.

Correct Answer: (d) 39 years
Solution:

Let the present age of P and Q be 3x years and 4x years

Q's age after 4 years = 4x + 4

R's age after 4 years = (4x + 4)/4 × 5 = 5x + 5

R's present age = 5x + 5 − 4 = 5x + 1

S's present age = 5x + 9

According to the question,

⇒ 3x + 4x + (5x + 1) + (5x + 9) = 28 × 4

⇒ 17x + 10 = 112

⇒ 17x = 102

⇒ x = 6

∴ S's present age = 5 × 6 + 9 = 39 years

3. If double the age of the daughter is added to the age of her mother, the sum is 70 and if double the age of mother is added to the age of the daughter, the sum is 95. The respective ages of daughter and mother (in years) are:

Correct Answer: (a) 15 and 40
Solution:

3. (e): Let the age of daughter be x years and the age of mother be y years

⇒ 2x + y = 70 ...(1)

and x + 2y = 95 ...(2)

By solving these equations we get, 3x = 45

⇒ x = 15

∴ from equation (1), we get,

y = 70 − 2 × 15

⇒ y = 40

∴ The respective ages of daughter and mother are 15 and 40 years.

4. There is a group of 3 people, Ajay, Raj and their teacher. The age of teacher is 1.5 times the age of Ajay and Raj is 5 years older than Ajay. If the average age of group is 25 years, then find the ratio of ages of Ajay and Raj.

Correct Answer: (c) 4:5
Solution:

Let Jay's age be x years

⇒ Teacher's age = 1.5x

And raj's age = x + 5

∴ According to question,

x + 1.5x + x + 5 = 25 × 3

⇒ 3.5x + 5 = 75

⇒ 3.5x = 75 − 5

⇒ x = 70/3.5

⇒ x = 20 years

∴ Teacher's age = 1.5 × 20 = 30 years
Ajay's age = 20 years
And raj's age = 20 + 5 = 25 years

∴ Required ratio = 20:25 = 4:5
∴ The ratio of ages of ajay and raj = 4:5

5. The average age of the family of 4 members is 38 years. If the age of the youngest member is 20 years, then find the average age of the family at the time of the birth of the youngest member.

Correct Answer: (d) 24 years
Solution:

Total age of the family
⇒ 38 × 4 = 152 years

Age before 20 years
⇒ 152 − 20 × 4
⇒ 152 − 80 = 72

The average age of the family at the time of the birth of the youngest member is

⇒ 72/3 = 24 years

∴ The average age of the family at the time of the birth of the youngest member is 24 years.

6. The ratio of the ages of Khushi and her Aunt is 1 : 4 and the ratio of the ages of Khushi's Aunt and her brother is 9 : 1. If Khushi's brother is 5 years younger than Khushi. What will be the age of Khushi's Aunt after 6 years?

Correct Answer: (c) 42 years
Solution:

Khushi : her Aunt = 1 : 4
Her Aunt : Her brother = 9 : 1

∴ Khushi : her Aunt : her brother = 9 : 36 : 4

∴ According to the question,
⇒ 9x − 4x = 5
⇒ 5x = 5
⇒ x = 1

Khushi's Aunt's age after 6 years = (36 × 1) + 6
= 42 years

∴ Khushi's Aunt's age after 6 years is 42 years.

7. The present age of mother is four times the present age of her son. 6 years hence, the ratio of ages of mother and son becomes 16:5. If x is the square of the present age of son, then what will be the value of (x+2)?

Correct Answer: (c) 1097/4
Solution:

Let the mother's age = m
And son's age = s

Then, m = 4s

Now, 6 years hence, age of mother = m + 6
And age of son = s + 6

∴ According to question,

(m + 6)/(s + 6) = 16/5

⇒ (4s + 6)/(s + 6) = 16/5

⇒ 20s + 30 = 16s + 96

⇒ 4s = 66

⇒ s = 33/2

Now, it is given that x is square of age of son.

∴ x + 2 = (33/2)² + 2
⇒ 1089/4 + 2
⇒ 1097/4

∴ The required value of x + 2 is 1097/4

8. In a group of 4 cousins, Vivek's present age is 4/5 of Palak's age. The ratio of ages of Palak and Hima is 2:1 and the present age of Rohit is 1.5 times of Vivek. If the average age of group is 35 years then what will be the age of Vivek?

Correct Answer: (a) 32 years
Solution:

Let the ratio of ages of palak and hima be x

Then, palak's age = 2x years and that of hima = x years

∴ Vivek's age = 4/5 × 2x = 8x/5

And rohit's age = 3/2 × 8x/5 = 24x/10

Now, according to question,

(2x + x + 8x/5 + 24x/10)/4 = 35

⇒ (2x + x + 8x/5 + 24x/10) = 140

⇒ (30x + 16x + 24x)/10 = 140

⇒ 70x = 1400

⇒ x = 20

∴ Vivek's age = 4/5 × palak's age
= 4/5 × 2 × 20 = 32

∴ Vivek's age is 32 years.

9. The total number of pupils in three classes of a school is 333. The number of pupils in classes I and II are in the ratio 3 : 5 and those in classes II and III are in the ratio 7 : 11. Find the number of pupils in the class that had the highest number of pupils.

Correct Answer: (c) 165
Solution:

Ratio of Pupils in class I and II = 3 : 5 ...(1)

Ratio of Pupils in class II and III = 7 : 11 ...(2)

To find the ratio for all the three class, we will have to make the ratio of Class II common for both the given ratio.

Multiply equation (1) by 7 and equation (2) by 5

∴ Ratio of Pupils in class I and II = 21 : 35

∴ Ratio of Pupils in class II and III = 35 : 55

So, pupils in class I, II and III are in ratio 21 : 35 : 55

Let the common multiplying factor be x

So, no. of pupils in these classes are 21x, 35x, 55x respectively.

Total no. = 333 = 21x + 35x + 55x

⇒ 111x = 333 ⇒ x = 3

Looking at the proportion, highest no. of pupils are in class III.

∴ No. of pupils in class III = 55x = 55 × 3 = 165

10. Laxman's father is 5 times the age of Laxman. 4 years ago Laxman's father was 7 times the age of Laxman. Find the present age of Laxman.

Correct Answer: (e) 12 years
Solution:

Let the present age of Laxman be x years

The present age of his father = 5x years

Ages of Laxman and his father 4 years ago would be
(x − 4) and (5x − 4) years respectively.

According to given information, 4 years ago father's age was 7 times the age of Laxman.

7 × (x − 4) = 5x − 4

7x − 28 = 5x − 4

2x = 24

x = 12 years

∴ Present age of Laxman is 12 years.