BANK & INSURANCE (PERCENTAGE) PART 3

Total Questions: 60

11. Income of Raju is 50% more than expenditure of Chutki. Chutki spends 40% of her income on rent, 20% of the remaining on clothes and 50% of the remaining (after spending on rent and clothes) on other necessities and saves the rest. If the amount saved by her in a particular was Rs. 12,000, then find the income of Raju.

Correct Answer: (d) Rs. 57,000 
Solution:Let the income of Chutki be Rs. ‘100x’
Amount spent on rent = 100x × 0.40 = Rs. ‘40x’
Amount spent on clothes
= (100x - 40x) × 0.20 = Rs. ‘12x’
Amount spent on other necessities
= (100x - 40x - 12x) ÷ 2 = Rs. ‘24x’
And amount saved = Rs. ‘24x’
ATQ:
24x = 12000
Or, x = 500
So, total expenditure of Chutki = 100x - 24x = 76x
= 76 × 500 = Rs. 38,000
So, income of Raju = 38000 × 1.50 = Rs. 57,000

12. The incomes of ‘A’ and ‘B’ is Rs. 7,500 and Rs. 6,000, respectively. ‘A’ spends 44% of his income and saves the rest. ‘B’ spends ___ of his income and saves the rest. The average of the savings of ‘A’ and ‘B’ is Rs.__.

The values given in which of the following options will fill the blanks in the same order in which it is given so as to make the statement true?
I. 35%, 4050  II. 40%, 3800  III. 28%, 4260

Correct Answer: (e) Only I and III
Solution:

Expenses of ‘A’ = 7500 × 0.44 = Rs. 3,300
So, savings of ‘A’ = 7500 - 3300 = Rs. 4,200

From I:
Savings of ‘B’ = 6000 × (1 − 0.35) = Rs. 3900
So, average of savings of ‘A’ and ‘B’ = (4200 + 3900) ÷ 2 = Rs. 4,050
So, I is true.

From II:
Savings of ‘B’ = 6000 × (1 − 0.4) = Rs. 3,600
So, average of savings of ‘A’ and ‘B’ = (4200 + 3600) ÷ 2 = Rs. 3,900 ≠ 3800
So, II is false.

From III:
Savings of ‘B’ = 6000 × (1 − 0.28) = Rs. 4,320
So, average of savings of ‘A’ and ‘B’ = (4200 + 4320) ÷ 2 = Rs. 4,260
So, III is true.

13. Savings of ‘B’ is (1/3)rd the expenditure of ‘A’, whereas income of ‘A’ is twice the expenditure of ‘B’. If income of ‘B’ is Rs. 3,000 more than savings of ‘A’ and the sum of expenditures of ‘A’ and ‘B’ is Rs. 7,500, then find the total savings of ‘A’ and ‘B’

Correct Answer: (d) Rs. 3,000 
Solution:Let the income of ‘A’ be Rs. ‘2y’
So, expenditure of ‘B’ = 2y ÷ 2 = Rs. ‘y’
Let the expenditure of ‘A’ be Rs. ‘3x’
So, savings of ‘B’ = 3x ÷ 3 = Rs. ‘x’
ATQ:
2y - 3x + 3000 = y + x
Or, 3000 = 4x - y … (I)
Also, y + 3x = 7500 … (II)
On adding equation (I) and (II), we have:
7x = 10500
Or, x = 1500
Putting x = 1500 in equation (I), we have
Or, y = 4 × 1500 - 3000
So, y = 3000
Savings of ‘B’ = 1500
Savings of ‘A’ = 2y - 3x = 2 × 3000 - 3 × 1500 = 1500
So, required sum = 1500 + 1500 = Rs. 3,000

14. ‘A’ saves 52% of his income. ‘B’ spends same amount as ‘A’ while savings of ‘B’ is Rs. 3,600 more than that of ‘A’. Find the percentage by which income of ‘B’ is more than that of ‘A’ given that if ‘A’ decreases his expenditure by Rs. 1,600, then he would be able to save (11/15)th part of his income.

Correct Answer: (d) 48% 
Solution:

Let income of ‘A’ be Rs. ‘100x’
So, savings of ‘A’ = 0.52 × 100x = Rs. ‘52x’
And, expenditure of ‘A’ = 100x - 52x = Rs. ‘48x’
ATQ:
48x - 1600 = (4/15) × 100x
Or, 720x - 24000 = 400x
Or, 320x = 24000
Or, x = 75
So, expenditure of ‘A’ = 52 × 75 = Rs. 3,600
So, savings of ‘B’ = 3600 + 3900 = Rs. 7,500
Income of ‘B’ = 7500 + 3600 = Rs. 11,100
Income of ‘A’ = 75 × 100 = Rs. 7,500
Required percentage
= [(11100 - 7500)/7500] × 100 = 48%

15. Directions (15-16): Study the following information carefully and answer the related questions.

Following data represents the number of employees in four companies A, B, C and D. In each company each employee works in either shift I or shift II. 60%, 40%, 75% and 50% respectively employees in company A, B, C and D are males. The average of number of employees who work in shift I in company A and B together is 305, in company B and C together is 375, in company C and A together is 320 and in company A and D together is 205.

Ques. If the ratio of employees who work in shift I to shift II from company A and D is 1:1 and 2 : 3 respectively, then what is the difference between the number of female employees in company A and D?

Correct Answer: (e) None of these
Solution:

Number of employees who work in shift I:
A + B = 2 × 305 = 610 ⇒ A = 610 - B
B + C = 2 × 375 = 750 ⇒ C = 750 - B
C + D = 2 × 275 = 550
A + C = 2 × 320 = 640
Then, 610 - B + 750 - B = 640
B = 360
A = 610 - 360 = 250
C = 750 - 360 = 390
D = 550 - 390 = 160
Number of employees who work in shift I from company A = 250
Number of employees who work in shift I from company D = 160
Number of employees who work in shift II from company A = 250 × 1/1 = 250
Number of employees who work in shift II from company D = 160 × 3/2 = 240
Total employees in company A = 250 + 250 = 500
Total employees in company D = 160 + 240 = 400
Then, number of female employees in company A = (100 - 60)% of 500 = 200
And, number of female employees in company D = (100 - 50)% of 400 = 200
Therefore, difference = 200 - 200 = 0

16. If the respective ratio of number of male employees to the employees work in shift I from company C is 11:13 and the average of number of employees who work in shift II from company C and D is 120, then number of female employees in company C are approximately what percent of number of female employees in company D?

Correct Answer: (b) 63% 
Solution:Number of employees who work in shift I:
A + B = 2 × 305 = 610 ⇒ A = 610 - B
B + C = 2 × 375 = 750 ⇒ C = 750 - B
C + D = 2 × 275 = 550
A + C = 2 × 320 = 640
Then, 610 - B + 750 - B = 640
B = 360
A = 610 - 360 = 250
C = 750 - 360 = 390
D = 550 - 390 = 160
Number of male employees in company C = 390 × 11/13 = 330
Then, total number of employees in company C = 330 × 100/75 = 440
Number of female employees in company C = 440 - 330 = 110
Now, number of employees in company C who work in shift II = 440 - 390 = 50
And, number of employees in company D who work in shift II = 2 × 120 - 50 = 190
Total number of employees in company D = 160 + 190 = 350
Number of female employees in company D = 50% of 350 = 175
Therefore, percentage = (110/175) × 100 = 63% (approx.)

17. The total number of students in institute A is 87.5% of the total number of students in institute B and the total number of students in institute C is 25% more than that of institute B. If the average number of students in institutes A, B and C is 950, then find the average number of students in institutes A and C together?

Correct Answer: (a) 969 
Solution:

Let the total number of students in institute B = 8x
And the total number of students in institute A = 8x × 7/8 = 7x
The total number of students in institute C = 8x × 125/100 = 10x
The total number of students in institutes A, B and C = 950 × 3 = 2850

8x + 7x + 10x = 2850
25x = 2850
x = 114
The total number of students in institute A = 7 × 114 = 798
The total number of students in institute C = 10 × 114 = 1140
Required average = (798 + 1140)/2 = 969

18. Arun spends 20% of his income on food, 40% of the rest income is on travel. Amount spends by Arun on entertainment is twice of his savings. Finally, he spends Rs. 3360 on household use. Find the amount spends by Arun on Travel, if he saves 3/25 of his total income.

Correct Answer: (d) Rs. 8960
Solution:Let total income of Arun = 100a
Amount spend on food = 20% × 100a = 20a
Amount spends on travel = 40% × (100a - 20a) = 32a
Savings of Arun = 3/25 × 100a = 12a
Amount Spends by Arun on Entertainment = 2 × 12a = 24a
Amount spends by Arun on households = 100a - (20a + 32a + 12a + 24a) = 12a
Now, 12a = 3360
Value of a = 3360/12 = 280
Amount Spends by Arun on Travel = 32a = 32 × 280 = Rs. 8960

19. The ratio of the monthly salary of Amal and Vimal is 10:7 and the monthly salary of Divya and Raghav together is 25% more than the monthly salary of Vimal. Ratio of the annual salary of Vimal is double the annual salary of Divya. If the average monthly salary of Amal and Divya is Rs.10800, then find the difference between the annual salary of Amal and Raghav?

Correct Answer: (c) Rs.91200
Solution:

Amal = 10x, Vimal = 7x
2 × Divya × 12 = 7x × 12
Divya = 3.5x
Divya + Raghav = 125/100 × 7x
Raghav = 35x/4 - 3.5x = 5.25x
Amal + Divya = 10800 × 2
10x + 3.5x = 21600
x = 1600
Required difference
= 10 × 1600 × 12 - (5.25 × 1600 × 12)
= Rs. 91200

20. Arjun, babu, Kathir, Dinesh and Esther had a total of Rs.550 with them. Arjun had twice the sum that Kathir has. Babu has Rs.12.5 more than Kathir. Dinesh's share is equal to the sum of the amount that babu and Kathir have, Esther has 75% of the amount that Arjun and babu together have. Find the amount which is Arjun and Esther together has?

Correct Answer: (d) Rs.275 
Solution:

Let the amounts with Arjun, babu, Kathir, dinesh & Esther be Rs A, Rs. B, Rs. C, Rs. D & Rs. E respectively.
A + B + C + D + E = 550 ----(I)

ATQ
A = 2C
C = A/2 ----(II)
B = C + 12.5
B = A/2 + 12.5
B = (A + 25)/2 ----(III)
D = B + C
D = (A + 25)/2 + A/2
D = (2A + 25)/2 ----(IV)
E = 3/4 (A + B)
E = 3/4 (A + (A+25)/2)
E = 3/8 (3A + 25) ----(V)

Substitute all values corresponding to A
A + (A + 25)/2 + A/2 + (2A + 25)/2 + 3/8 (3A + 25)
(8A + 4A + 100 + 4A + 8A + 100 + 9A + 75)/8
= 550
33A + 275 = 4400
A = 125
Arjun = Rs. 125
Esther = 3/8 (3 × 125 + 25) = Rs. 150
Arjun + Esther = Rs. 275