BANK & INSURANCE (RATIO AND PROPORTION) PART 2

Total Questions: 70

11. Two years ago the ratio of annual salary of three friends P, Q and R is 4 : 3 : 5. Every year since then the salary of P, Q and R increases by 10%, 12% and 50% respectively. If the present monthly salary of P is 19,360, then what was the monthly salary of R one year ago?

Correct Answer: (c) Rs. 30,000
Solution:

Ratio of annual salary of P, Q and R 2 years ago = 4 : 3 : 5

Increment of salary of P, Q and R per year respectively

= 10%, 12% and 50%

Present monthly salary of P = Rs. 19,360

Let annual salary of P, Q and R two years ago = 4x, 3x and 5x respectively

Present salary of P = Rs. 19,360 (given)

So,

4x×(110/100)×(110/100)×(1/12)=19,3604x × (110/100) × (110/100) × (1/12) = 19,3604x×(110/100)×(110/100)×(1/12)=19,360

⇒ 121x/300 = 19,360

⇒ x = (19360 × 300)/121

⇒ x = Rs. 48,000

R’s annual salary two years ago = 5x = 5 × 48,000

= Rs. 2,40,000 p.a.

R’s annual salary one years ago

= 2,40,000 × 150/100 = Rs. 3,60,000 p.a.

R’s monthly salary one year ago

= 360000 / 12

= Rs. 30,000

∴ R’s monthly salary one year ago was Rs. 30,000

12. In 240 litre mixture, 200 litre is milk and rest is water. If 30 litre mixture is taken out and 5 litre milk and 5 litre water is added again, then find the quantity of milk in final mixture.

Correct Answer: (c) 180 litre
Solution:

Initial Mixture = 240 litre
Milk in initial mixture = 200 litre
Water in initial mixture = 40 litre
Mixture taken out = 30 litre
Water added = 5 litre
Milk added = 5 litre

Calculation:
Ratio of milk and water in initial mixture = 200 : 40
⇒ Milk : Water = 5 : 1

In 30 litre mixture taken out ratio of milk and water is 5 : 1

Let milk removed be 5x litre and water removed be x litre

⇒ 5x + x = 30
⇒ 6x = 30
⇒ x = 5

Milk removed = 5x = 5 × 5
⇒ Milk removed = 25 litre

Water removed = x = 5 litre

Milk in mixture after removal = 200 − 25 = 175 litre

5 litre more milk is added

⇒ Quantity of milk in final mixture = 175 + 5

∴ The quantity of milk in the final mixture is 180 liter

13. 630 students of a school took an exam. The ratio of boys to girls who took the exam is 3:4. The ratio of number of students passed the exam to those who failed the exam is in the ratio 11:3. Among the girls, the ratio of number of students who passed to those who failed the exam is in the ratio is 11:4. Find the ratio of number of boys to the number of girls who failed?

Correct Answer: (e) 13:32
Solution:

No. of students = 630

No. of boys = 630 × 3/7 = 270
No. of girls = 360

Total passing students = 630 × 11/14 = 495

Total failing students = 630 − 495 = 135

Total girls passing = 11/15 × 360 = 264

So no. of boys passing = 495 − 264 = 231

No. of girls failing = 360 − 264 = 96

And boys failing = 270 − 231 = 39

Required ratio = 39 : 96 = 13 : 32

14. A person has three daughters, namely Aparna, Vrinda and Divya. He gave some amount of money to each of them such that Vrinda got 4/3 times the amount that Aparna got, while Divya got 5/4 times the amount that Vrinda got. If every one of them spent Rs. 100 then the ratio of remaining money with Aparna, Vrinda and Divya would be in the 1:2:3 respectively. What will be the average amount per person after all three receive another Rs. 700 each from their father?

Correct Answer: (c) Rs. 900
Solution:

Let the amount with Aparna be Rs. x

Amount with Vrinda = 4x/3

Amount with Divya = 4x/3 × 5/4 = 5x/3

x − 100 : 4x/3 − 100 : 5x/3 − 100 = 1 : 2 : 3

x − 100 : (4x − 300) = 1/6

x = 150

Amount with Aparna, Vrinda and Divya will be

Rs.150, Rs.200 and Rs.250

Total amount received from father = 700 × 3 = Rs.2100

Total amount with the 3 sisters = 150 + 200 + 250 + 2100 = 2700

Average amount per person = 2700/3 = Rs.900

15. The ratio of the ages between Avani and Bindu is 6:5. The difference between the ages of Chandu and Avani is more than 5 years. The age of Durga is a prime number between the ages of Avani and Chandu. The ratio of the ages of Bindu and Chandu is 2:3. If the ages of all four are integers, what is the minimum possible difference between the ages of Chandu and Durga?

Correct Answer: (b) 1
Solution:

Suppose the ages of Avani, Bindu, Chandu and Durga be a, b, c and d respectively.

a : b = 6 : 5; c − a > 5; d = prime number between the ages of Avani and Chandu.

Also, b : c = 2 : 3

So, a : b : c = 12 : 10 : 15

To satisfy the condition required, multiply the ratio by 2.

Thus, a : b : c = 24 : 20 : 30

Let Avani's age be 24 years, Bindu's age be 20 years and Chandu's be 30 years.

Now, the difference in the ages of Avani and Chandu is greater than 5.

Now, the age of Durga is a prime number between the ages of Avani (a = 24) and Chandu (c = 30)

It means, d = 29

Hence, required difference between c and d = 30 − 29

= 1 year

16. A group of 10 men and 12 women were going to Russia for a conference. A week before their departure, equal number of men and women joined them and the ratio of the total number of men and women became 6:7. Also, just one day before their departure, equal number of men and women left them. The new ratio between the number of men and women was 4:5. What was the final strength of the group that went for the conference?

Correct Answer: (c) 8 men and 10 women
Solution:

Let x be the number of men who joined the group.

Thus,

(10 + x) / (12 + x) = 6/7

So, x = 2

Now the number of men and women become 12 and 14 respectively.

Now,

(12 − y) / (14 − y) = 4/5

So, y = 4

Now the number of men and women become 8 and 10 respectively.

17. The ratio of number of laptops manufactured and sold by a company in the year 2014 is 13:11, respectively. In 2015, 17,700 laptops were manufactured by the company and ratio of number of laptops sold to unsold was 11:9, respectively. If in 2015 the number of laptops sold was 2000 unit more than unsold laptops then what was the number of laptops manufactured in 2014? (Consider that the number of unsold laptops in 2014 were included in 2015 to be sold and the company started manufacturing laptops in 2014 only.)

Correct Answer: (a) 14,950
Solution:

Let number of laptops sold in 2015 = 11x

Then number of laptops unsold in 2015 = 9x

According to question,

11x − 9x = 2000

⇒ 2x = 2000

⇒ x = 1000

Total number of laptops in 2015 = 20,000

Since, only 17,700 laptops were manufactured in 2015

So, unsold laptops of 2014 = 20000 − 17700 = 2300

Let, the number of laptops manufactured in 2014 = 13y

So, number of laptops sold in 2014 = 11y

Therefore,

13y − 11y = 2300

⇒ 2y = 2300

⇒ y = 1150

Therefore, number of laptops manufactured in 2014

= 13y = 13 × 1150 = 14,950

18. The ratio of weight of water present to the weight of cotton in a cloth was 2:3 before it was taken for drying up under the sun. The water evaporated from the cloth at the rate of 20 g/min but after 8 minutes rain began and the cloth stopped drying instead, rain wetted cloth at the rate of 30 gm/min. If ratio of weight of water present in the cloth to weight of cotton became 17:15 after 18 minutes of when it was taken for drying up then find the weight of cotton in the cloth.

Correct Answer: (b) 300 g
Solution:

Let weight of water present in the cloth and weight of cotton be 2x and 3x

Amount of water evaporated due to sun = 20 × 8 = 160 g

Amount of water added by rain = 30 × 10 = 300 g

So, water present in the cloth after 18 minutes

= 2x − 160 + 300 = (2x + 140) g

According to question,

(2x + 140) / 3x = 17/15

⇒ 30x + 2100 = 51x

⇒ 21x = 2100

⇒ x = 100

So, weight of cotton = 3 × 100 = 300g

19. In Punjab, any person consuming energy has to pay a fixed charge and an additional amount proportional to the energy (in kilowatt (kwh)) consumed and if a person consumes more than 60 kwh per month, one has to pay an amount proportional to the square root of energy consumed (in kwh) in addition to the first additional amount. If a person pays Rs.400 for 50 kwh, Rs.360 for 30 kwh and Rs.498 for 81 kwh, how much should he pay for 100 kwh (in Rs.)?

Correct Answer: (d) Rs. 540
Solution:

Let the total amount paid = x

Fixed charge = y

Kilowatt (kwh) consumed = n

If anyone consumes less than 60 kwh per month, then

Amount paid (x) = fixed charge (y) + k1 × (number of kwh consumed)

Where k1 is the constant of proportionality

x = y + k1 × n

According to question,

400 = y + 50 × k1 ........(i)

360 = y + 30 × k1 ........(ii)

If anyone consumes more than 60 kwh per month, then

x = y + (k1 × n1) + (k2 × √n), where k2 is the constant of proportionality

Now, 498 = y + (81 × k1) + (√81 × k2)

498 = x + (81 × k1) + (9 × k2) ........ (iii)

After solving (i) and (ii), we get

20 × k1 = 40 ⇒ k1 = 2 and y = (400 − 50 × 2) = 300

Substituting the value of y and k1 in (iii), we get

498 = 300 + (81 × 2) + (9 × k2)

⇒ 9 × k2 = (498 − 462)

⇒ 9 × k2 = 36

⇒ k2 = 4

Thus, amount to be paid for using 100 kwh is

x = 300 + (100 × 2) + (√100 × 4)

= 300 + 200 + (4 × 10)

= Rs. 540

20. The ratio of number of male employees to female employees in a company was 35:29. Total 70 employees left the job in which ratio of male to female employees was 11:3 and then company recruited more employees in which the ratio of male and female employees was 5:8 and resultant ratio of male to female employees became 139:129. Leaving the rest of conditions the same, if 70 employees did not leave the company the resultant ratio of male to female employees would have been 25:22 after the recruitment. Find the number of female recruited by the company.

Correct Answer: (e) 80
Solution:

Let number of male and female employees initially were 35x and 29x respectively.

Case I: 70 employees left the company

Number of male employees left the company

= 11/14 × 70 = 55

Number of male employees remained in the company

= 35x − 55

Number of female employees left the company

= 70 − 55 = 15

Number of female employees remained in the company

= 29x − 15

Case II: company recruited more employees in which the ratio of male to female employees was 5 : 8

Let number of male and female employees recruited by the company be 5y and 8y

Number of male employees after recruiting 130 more employees

= 35x + 5y − 55

Number of female employees after recruiting 130 more employees

= 29x + 8y − 15

Given,

(35x + 5y − 55) / (29x + 8y − 15) = 139/129

4515x + 645y − 7095 = 4031x + 1112y − 2085

484x − 467y = 5010 .......... (i)

Also,

(35x + 5y) / (29x + 8y) = 25/22

770x + 100y = 725x + 200y

45x = 90y

x = 2y .......... (ii)

From (i) and (ii)

968y − 467y = 5010

501y = 5010

y = 10

Number of female employees recruited by the company

= 8y = 80