BANK & INSURANCE (RATIO AND PROPORTION) PART 2

Total Questions: 70

61. The ratio of males and females in a city is 7 : 8 respectively and the percentage of children among males and females is 25% and 20% respectively. If the number of adult females in the city is 1, 56, 800. What is the total population?

Correct Answer: (b) 367500
Solution:

Let no. of males and females be 7x and 8x.

Percentage of children among females = 20%

So, 80% of females are adults,

(80/100) (8x) = 156800

x = 156800 × (100 / (80 × 8)) = 24500

Total population = 7x + 8x = 15x = 15(24500)

= 367500

62. A man leaves Rs. 8600 to be divided among 5 sons, 4 daughters and 2 nephews. If each daughter receives four times as much as each nephew and each son receives five times as much as each nephew, how much does each daughter receive?

Correct Answer: (c) Rs. 800
Solution:

Let each nephew receives Rs. x

Son : Daughter : Nephew = 5x : 4x : x

5 sons : 4 daughters : 2 Nephews = 25x : 16x : 2x

And 25x + 16x + 2x = Rs. 8600

43x = Rs. 8600

x = Rs. 200

Required answer = 4 × 200 = Rs. 800

63. A man ordered a pairs of black socks and some pairs of brown socks. The price of a black socks is double that of a brown pair. While preparing the bill the clerk interchanged the number of black and brown pairs by mistake which increased the bill by 50%. The ratio of the number of black and brown pairs of socks in the original order was?

Correct Answer: (b) 1 : 4
Solution:

Number of brown socks = x

Price of brown socks = Rs. y per pair

Price of black socks = Rs. 2y per pair

4y + x × 2y

(150 / 100) (4 × 2y + xy) = 4 + 2x = 3/2 (8 + x)

= 8 + 4x = 24 + 3x

4x = 24 − 8 = 16

Required ratio = 4 : 16 = 1 : 4

64. A sum of money is to be distributed among P, Q and R in the ratio 6:19:7. If R gives Rs. 200 from his share to Q, the ratio of P, Q and R becomes 3:10:3. what is the total sum?

Correct Answer: (e) None of these
Solution:

Let the shares of P, Q and R be 6x, 19x and 7x.

By given condition, R’s new share = 7x − 200

Q’s new share = 19x + 200

New ratio = 6x : 19x + 200 : 7x − 200 = 3 : 10 : 3

P : R = 6x : 7x − 200 = 3 : 3

6x = 7x − 200

x = 200

Total sum = 6x + 19x + 7x = 32x = 6400

65. In a college the ratio of boys to girls is 31:23 respectively. When 75 more girls join the college this ratio becomes 124:107. How many more girls should join the college to make the number of boys and girls equal?

Correct Answer: (d) 85
Solution:

ATQ

31x / (23x + 75) = 124 / 107

⇒ x = 20

⇒ No. of boys = 31 × 20 = 620

and no. of Girls = 23 × 20 + 75 = 535

∴ No. of more Girls required = 620 − 535 = 85

66. The value of a diamond is directly proportional to the square of its weight. A diamond unfortunately breaks into three pieces with weights in the ratio 3:4:5 thus a loss of Rs.9.4 lakh is incurred. What is the actual value of the diamond?

Correct Answer: (c) 14.4 lakh
Solution:

The ratio of broken parts by weight = 3x : 4x : 5x

Therefore value of broken parts of diamond

= (3x)² + (4x)² + (5x)² = 50x²

The value of original diamond = (3x + 4x + 5x)²

= 144x²

Therefore, loss in value = 144x² − 50x² = 9.4 lakh

94x² = 940000

x² = 10000

Hence the actual value of the diamond = 144x²

= 144 × 10000 = 14.4 lakh

67. A canister holds 36 liters of mixture of milk and water in the ratio 3:1. 15 liters of milk is added to the canister. The new ratio of the mixture is:

Correct Answer: (b) 14:3
Solution:

Milk : water = 3 : 1

Quantity of Milk = 36 × 3/4 = 27 litres

Quantity of water = 36 × 1/4 = 9 litres

When 15 litres of milk is added then,

Milk = 27 + 15 = 42 litres

Required ratio = 42 : 9 = 14 : 3

68. Parthi, Thyagu and Kavin enter into a partnership. Parthi invests 5 times as much as Thyagu's investment and Thyagu invests 3/7th of Kavin's investment. If the total profit at the end of the year is Rs. 112500, then find the share of Thyagu?

Correct Answer: (c) Rs. 13500
Solution:

The investment of Parthi and Thyagu = 5 : 1

Thyagu’s investment = (3/7) × Kavin’s investment

The investment of Thyagu and Kavin = 3 : 7

The investment of Parthi, Thyagu and Kavin

= 15 : 3 : 7

Here, the period is not given.

So, The ratio of investment = The ratio of profit

Total profit = Rs. 112500

25’s = 112500

1’s = 4500

The share of Thyagu = 3’s = Rs. 13500

69. P, Q and R invested in the ratio of 6 : 5 : 9. After 5 months, Q invested the same amount as before but P and R withdraw 2/7th and 1/3rd of the initial investment respectively. Find the share of R, if the total profit at the end of the year is Rs. 108900?

Correct Answer: (d) Rs. 39150
Solution:

The share of P, Q and R,

= [6×5 + 6×(5/7)×7] : [5×5 + 10×7] : [9×5 + 9×(2/3)×7]

⇒ [30 + 30] : [25 + 70] : [45 + 42]

= 60 : 95 : 87

242’s = 108900

1’s = 450

The share of R = 87’s = Rs. 39150

70. A, B and C entered into a partnership by investing in the ratio of 4 : 2 : 3. At the end of the year, the total profit is in the ratio of 12 : 4 : 9. Find the ratio of period of time they invested in the business?

Correct Answer: (a) 3 : 2 : 3
Solution:

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Thank you for your response. ✨

The ratio of investment = 4 : 2 : 3

The ratio of profit = 12 : 4 : 9

Ratio of investment × Ratio of Period = The ratio of Profit

Ratio of Period = The ratio of Profit / Ratio of investment

According to the question,

= (12/4) : (4/2) : (9/3)

= 3 : 2 : 3