BANK & INSURANCE (RATIO AND PROPORTION) PART 2

Total Questions: 70

21. 8 years ago Ankush's age was two times of his daughter's age one year back. Ankush's mother's present age is 7/3 times the present age of Ankush. Two years from now, Ankush's mother's age will be five times the age of her granddaughter. Find the ratio of the present ages of Ankush's daughter, Ankush and Ankush's mother.

Correct Answer: (a) 9:21:49
Solution:

Let father's age be x years and his daughter's age be y years.

x − 8 = 2(y − 1)

x − 2y = 6 .......... (i)

Grandmother's age = 7/3x

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

7x − 15y = 24 .......... (ii)

On solving the above equations y = 18, x = 42

Therefore, daughter's age = 18 years, father's age = 42 years and grandmother's age = 7/3 × 42 = 98 years

Required ratio = 18 : 42 : 98 = 9 : 21 : 49

22. The ratio of present age of Kamal and present age of Vimal is 2:3, respectively and ratio of present age of Kamal and present age of Vimal's son is 4:1, respectively. At the time of the marriage of Vimal, the ratio of age of Kamal and age of Vimal was 4:7, respectively and Vimal's son was born after 2 years of his marriage. Find the present age of Vimal's son.

Correct Answer: (b) 6 years
Solution:

Let, present age of Vimal's son

Then, 2x = 4y

⇒ x = 2y

Let, age of Kamal and Vimal at the time of the marriage of Vimal was 4z and 7z respectively.

If Vimal's age was 7z at the time of his marriage then his present is now past 2 years in addition to the age of his son.

So, 7z + 2 + y = 3x

⇒ 7z + 2 + y = 6y

⇒ 7z + 2 = 5y

⇒ y = (7z + 2)/5

And, 4z + 2 + y = 2x

⇒ 4z + 2 + y = 4y

⇒ 4z + 2 = 3y

⇒ 4z + 2 = 3(7z + 2)/5

⇒ 20z + 10 = 21z + 6

⇒ z = 4

Therefore, y = (7z + 2)/5 = 6 years

So, present age of Vimal's son = 6 years

23. In a company, there are 80 IT employees, 60 HR employees, 100 Marketing employees and 40 Sales employees. Ratio of the number of male to female IT employees in a company is 3:1 and the ratio of the number of male to female HR employees in a company is 2:1. If the male employees of marketing department is 20 more than that of the number of female employees in marketing department and the half of the employees in sales department are male, then what is the ratio of the total number of male to female employees from a company?

Correct Answer: (d) 9:5
Solution:

Male IT employees = 80 × 3/4 = 60

Female IT employees = 80 × 1/4 = 20

Male HR employees = 2/3 × 60 = 40

Female HR employees = 1/3 × 60 = 20

Male employees in marketing = 40 + 20 = 60

Female employees in marketing = 40

Male employees in sales = 40/2 = 20

Female employees in sales = 40/2 = 20

Required ratio =

(60 + 40 + 60 + 20) : (20 + 20 + 40 + 20)

= 180 : 100 = 9 : 5

24. The ratio of the number of male to female in Chennai and Bangalore is 3:2 and 7:3 respectively. If 20% of the male from Chennai are undergraduate and 60% female from Bangalore are postgraduate. If the postgraduate males from Chennai and postgraduate female from Bangalore is 3300 and the total number of people in Chennai and Bangalore is equal, then what is the total male population in Chennai and Female population in Bangalore?

Correct Answer: (a) 4500
Solution:

Number of male in Chennai = 3x

Number of female in Chennai = 2x

Number of male in Bangalore = 7y

Number of female in Bangalore = 3y

Number of population is equal in Chennai and Bangalore

3x + 2x = 7y + 3y

x = 2y

Number of postgraduate male in Chennai

= 80/100 × 3x = 2.4x

Number of postgraduate female in Bangalore

= 60/100 × 3y = 1.8y

2.4x + 1.8 × (x/2) = 3300

4.8x + 1.8x = 6600

x = 1000

Male population in Chennai and Female population in Bangalore

= 3x + 3y = 3x + (3 × x/2)

= 4.5x

Required total = 4.5 × 1000 = 4500

25. An alloy A is formed by mixing gold and silver in the ratio 2 : 1. Another alloy B is formed by mixing silver and platinum in the ratio 3 : 4. An alloy C is obtained by mixing alloys A and B in a certain ratio such that the ratio of gold and platinum in alloy C is 5 : 6. Which of the following correctly represents the share of silver in alloy C?

Correct Answer: (d) 49/126
Solution:

We have been given that alloy A contains gold and silver in the ratio 2 : 1.

Let there be 21x units of A. So it will have 14x units of gold and 7x units of silver.

Let there be 21y units of alloy B.

So we have 9 units of silver and 12 units of platinum.

Let these two be mixed to get the desired alloy.
Hence, the total amount of gold in alloy C will be 14x and total amount of platinum will be 12y.

We have been given that

14x / 12y = 5 / 6

⇒ 84x = 60y ⇒ x / y = 5 / 7

Thus alloys A and B must have been mixed in the ratio 5 : 7

Thus, the share of silver in the final mixture

(35 + 63) / (252) = 98 / 252 = 49 / 126

26. The average score in an examination taken by 52 students of a class is 85. If the scores of the best 5 performers are not considered, the average score of the remaining students falls by 2. If, none of the first five highest scorers is not below 80 and if each of the 5 top scorers had distinct integral scores, find the maximum possible score of the topper.

Correct Answer: (d) 193
Solution:

Let the score of the topper be T.

Total score of the 52 students = 52 × 85 = 4420

Total score of the remaining 47 students after scores of the best five performers are removed
= 47 × 83 = 3901

Total score of the top five students
= 4420 − 3901 = 519

T + (total score of the next 4 top scores) = 519

T is the maximum when the total score of the next 4 top scorers is minimum.

Total score of the next 4 top scorers has a minimum value of
80 + 81 + 82 + 83 = 326 (since all the top 5 scores are distinct) and the least is 80.

T has a maximum value of 519 − 326 = 193

27. A father distributed some chocolates among his four children and kept some with him. The eldest three children got chocolates in the ratio 3 : 11 : 7. The total number of chocolates with father and youngest child is three times the total chocolates with the three eldest children. The ratio of chocolates with father and that with all the children is 3 : 4. Find the total number of chocolates if the youngest child had 81 chocolates with him?

Correct Answer: (b) 252
Solution:

Let the children be P, Q, R and S and Father be F

Chocolates with P : Q : R = 3 : 7 : 11

Let the number of chocolates be 3k, 7k and 11k

Total chocolates with three eldest children = 21k

Chocolate with F and S = 3 × 21k = 63k

Total chocolates = (21k + 63k) = 84k

Chocolate with F : (P + Q + R + S) = 3 : 4

Total 7 units of chocolate = 84k

1 unit = 12k

Chocolate with F = 3 × 12k = 36k

Chocolate with S = (63k − 36k) = 27k

27k = 81 ⇒ k = 3

Total number of chocolates = 84k = 84 × 3 = 252

28. The monthly expenditure of Irfan is 40% less than that of Imran. If at the end of the month Imran and Irfan save Rs. 12,000 and Rs. 10,000 respectively, and the ratio of monthly income of Imran and Irfan is 8 : 5 respectively, then the yearly income of Imran is how much more than the yearly income of Irfan?

Correct Answer: (b) Rs. 504000
Solution:

Let the monthly income of Imran and Irfan is Rs. R and Rs. S respectively.

Then, according to the question

Ratio of their monthly income = R : S = 8 : 5

Let us assume it 8x and 5x, then the difference between their monthly income

⇒ 8x − 5x = 3x ...(i)

Let the monthly expenditure of Imran is Rs. 100a

Then the monthly expenditure of Irfan = Rs. 60a

Ratio of Imran’s and Irfan’s expenditures = 100a : 60a

= 5 : 3

According to question :

(8x − 12000) / (5x − 10000) = 5 / 3

⇒ 24x − 36000 = 25x − 50000

⇒ x = 14,000

∴ Required difference
= 3x = 3 × 14000 × 12 = Rs. 504000

29. Five years before, the age of father was 5 times of the age of son. Ten years hence, the age of father will become 2.5 times of the age of son. At present, what is the ratio of the sum of their ages and the difference of their ages?

Correct Answer: (b) 16 : 9
Solution:

5 years before, let the age of father = 5x then the age of son = x

At present, the age of father = 5x + 5 years and the age of son = x + 5

10 years hence, the age of father will become
5x + 5 + 10 = 5x + 15 and the age of son will become
= x + 5 + 10 = x + 15 years

According to the question

5x + 15 = 2.5(x + 15)

By solving, x = 9

At present, the age of father = 5x + 5 = 50 years and the age of son = x + 5 = 14

The required ratio = (50 + 14) : (50 − 14) = 64 : 36

= 16 : 9

30. A child paints a sphere with two colors yellow and blue making the ratio of yellow and blue area 1 : 3. If the ratio of yellow and blue area in the upper hemisphere is 4 : 9, the yellow area in lower hemisphere is what percent of the blue area in lower hemisphere?

Correct Answer: (d) 23.81%
Solution:

Ratio of yellow and blue = 1 : 3 (4 parts)

Ratio of yellow and blue in upper hemisphere = 4 : 9 (13 parts)

Let the total sphere be divided into 52 parts, then as per the ratio, the number of parts = 13 yellow and 39 blue parts

In upper hemisphere there will be 26 parts, as per the ratio (4 : 9), number of parts = 8 yellow and 18 blue parts

Number of parts in lower hemisphere = Total − upper hemisphere

Yellow parts = 13 − 8 = 5 parts and blue parts = 39 − 18 = 21 parts

Reqd. % = (5 / 21) × 100 = 23.81%