BANK & INSURANCE (RATIO AND PROPORTION) PART 3

Total Questions: 40

11. A's weight is 6 kg more than B's weight and B's weight is 15 kg less than C's weight. When A's weight is increased by 'm' kg, B's weight is increased by (m − 2) kg and C's weight is decreased by (m + 9) kg, ratio of A's weight to C's weight becomes 6 : 5 respectively and ratio of B's weight to C's weight becomes 16 : 15 respectively. Find the ratio of initial weights of A and B respectively?

Correct Answer: (b) 11 : 10
Solution:

Let initial weight of C = ‘x’ kg

So, initial weight of B = (x − 15) kg

And initial weight of A = x − 15 + 6 = (x − 9) kg

From the question:

[(x − 9) + m] / [x − (m + 9)] = 6/5

5x − 45 + 5m = 6x − 6m − 54

x − 11m = 9 ............(1)

And,

[(x − 15) + (m − 2)] / [x − (m + 9)] = 16/15

15x + 15m − 255 = 16x − 16m − 144

31m − x = 111 ............(2)

From equations (1) and (2):

20m = 120

m = 6, x = 75

Initial weight of A = 75 − 9 = 66 kg

Initial weight of B = 75 − 15 = 60 kg

Required ratio = 66 : 60 = 11 : 10

12. Iniyan has some amount and he distributed that amount to his son and daughter. When his son spends Rs.1170, then the ratio of the amount has by Son to Daughter is 3:14. If Rs.1170 spends by his Son and at the same time his daughter also spends Rs.6400, then the amount has by Iniyan's son to daughter becomes 1:3. What is the difference between the initial amount has by Iniyan's son and daughter?

Correct Answer: (d) Rs.12910
Solution:

Initial amount has Son = x

Initial amount has daughter = y

(x − 1170)/y = 3/14

3y = 14x − 16380

14x − 3y = 16380 ............(1)

(x − 1170)/(y − 6400) = 1/3

y − 6400 = 3x − 3510

y − 3x = 2890 ............(2)

From (1) and (2)

5x = 25050

x = 5010

y = 17920

Difference = 17920 − 5010 = Rs.12910

13. Two years ago, the ratio between Raghu's and Ravi's salary was 17:14. The ratio of their individual salaries between two years ago salary and this year's salaries are 17:25 and 7:10 respectively. At present, the total of their salary is Rs.22500. What is the present salary of Ravi?

Correct Answer: (c) Rs.10000
Solution:

Let the salaries of Raghu and Ravi two years before be A1, B1 and now be A2, B2 respectively.

A1/B1 = 17/14 ............(i)

A1/A2 = 17/25 ............(ii)

B1/B2 = 7/10 ............(iii)

A2 + B2 = 22500 ⇒ A2 = 22500 − B2 ............(iv)

(i) × (iii) ⇒ A1/B2 = 17/20 ............(v)

(ii)/(v) ⇒ B2/A2 = 4/5 ............(vi)

(iv) in (vi), B2/(22500 − B2) = 4/5

⇒ B2 = 10000

Present salary of Ravi = Rs.10000

14. Ratio of the number of male to female employees in company A and B is 3:2 and 7:3 respectively. If 20% of male employees from A are left and 40% of female employees from B are left the company, then remaining male employees in A and B together is 110, then find the total employees in A and B together initially?

Correct Answer: (e) Cannot be determine
Solution:

Total employees in A = x

Total employees in B = y

Male to female ratio in A = 2 : 3

Male to female ratio in B = 7 : 3

(2/5 × 80/100 × x) + (7/10 × 60/100 × y) = 110

We don’t know any values.

Data inadequate

15. In company A has two departments- IT and HR and the ratio of the number of male to female employees in A is 2:3. If the female employees work in HR department is 80% of the total number of employee works in HR department and the total number of employees in HR department is 50% more than the total number of employees works in IT department. If the total number of employees in A is 1600, then find the number of male employees in HR department?

Correct Answer: (c) 192
Solution:

Total employees = 1600

Number of male employees = 2/5 × 1600 = 640

Number of female employees = 3/5 × 1600 = 960

Number of employees in IT department = x

Number of employees in HR department

= x × 150/100

x + 3x/2 = 1600

5x = 3200

x = 640

Number of HR employees = 640 × 3/2 = 960

Number of female employees from HR department

= 960 × 80/100 = 768

Number of male employees HR department

= 960 × 20/100 = 192

16. If the ratio of the number of balls in box A and box B is 4:5 and the ratio of the balls in box C to D is 3:4. If the number of balls in box D is 4 less than the number of balls in B and the average number of balls in all the boxes together is 87, then what is the number of balls in box A?

Correct Answer: (d) 80
Solution:

Number of balls in A = 4x

Number of balls in B = 5x

Number of balls in D = 5x − 4

Number of balls in C = 3/4 × (5x − 4)

(4x + 5x + 5x − 4 + (15x − 12)/4) / 4 = 87

14x + 15x/4 = 87 × 4

71x = 1420

x = 20

Number of balls in A = 20 × 4 = 80

17. Ratio of the number of male to female employees in company A is 4:3 and the ratio of the number of male to female employees in B is 3:2. If 20 male employees from A shifted to B and 12 female employees from B is shifted to A, then the total number of employees in B is 98. If the initial number of male employees in B is 16 less than the total number of initial employees in A, then find the initial number of female employees in A?

Correct Answer: (c) 30
Solution:

Number of male employees in B = 3x

Number of female employees in B = 2x

3x + 20 + 2x − 12 = 98

5x = 90

x = 18

Total number of male employees in B = 3 × 18 = 54

Total number of employees in B = 54 + 16 = 70

Number of female employees in A = 70 × 3/7 = 30

18. If the number of female employees in company A is 50% more than the number of male employees in the same company and the number of female employees in company B is twice the number of male employees in the same company. If the total number of employees in A is 120 more than the number of employees in B, then what is the ratio of the number of male to female employees in A and B together?

Correct Answer: (d) Cannot be determine
Solution:

Number of male employees in A = x

Number of female employees in A = x × 150/100

= 3x/2

Total number of employees in A = x + 3x/2 = 5x/2

Number of male employees in B = y

Number of female employees in B = 2y

Total number of employees in B = 3y

5x/2 − 3y = 120

5x − 6y = 240

5x = 240 + 6y

We cannot find the answer.

19. Ratio of the red to yellow balls in box A is 3:5 and the ratio of the red to yellow balls in box B is 4:3. If the total red balls in box A and B together is 9 less than the total yellow balls in box A and B together, total number of balls in box A and B together is 69, then find the total number of red balls in both boxes together?

Correct Answer: (b) 30
Solution:

Total number of balls in A = 8x

Total number of balls in B = 7y

(5x + 3y) − (3x + 4y) = 9

2x − y = 9 ............(1)

8x + 7y = 69 ............(2)

(2) + (1) × 7

22x = 69 + 63

x = 6

y = 12 − 9 = 3

Total number of balls in B = 3 × 7 = 21

Red balls in box A = (8 × 6) × 3/8 = 18

Red balls in B = 21 × 4/7 = 12

Total red balls = 18 + 12 = 30

20. There are two friends Amit and Mishra each having particular number of gold coins. Amit said to Mishra that if you give 20 gold coins, mine will be twice as yours. For that Mishra replied if you give 90 coins, mine will be six times as yours. What is the number of gold coins Mishra having?

Correct Answer: (e) 90 coins
Solution:

Let x and y be the number of gold coins of Amit and Mishra respectively.

By data,
(x + 20) = 2x(y − 20)
x + 20 = 2y − 40
2y − x = 60 ............(1)

(y + 90) = 6x(x − 90)
y + 90 = 6x − 540
y − 6x = −630 ............(2)

After solving (1) and (2), we have
11y = 990
y = 90