BANK & INSURANCE (PERCENTAGE) PART 3

Total Questions: 60

1. In 3 villages v1, v2 and v3, the female population of the 3 villages are in the ratio of 2 : 3 : 4 respectively. In village v1, 55% of the female are working, in village v2, 25% of the female are working and in village v3, 50% of the female are working. Find the percentage of non – working female in the 3 villages.

Correct Answer: (c) 57.22% 
Solution:

Let the female population of v1, v2 and v3 be 2x, 3x and 4x respectively
Working female in village v1 = (55/100) × 2x = 1.1x
Working female in village v2 = (25/100) × 3x = 0.75x
Working female in village v3 = (50/100) × 4x = 2x
Total working female in all the three villages
= (1.1x + 0.75x + 2x) = 3.85x
Total female population all the three villages
= (2x + 3x + 4x) = 9x
Total non-working female all the three villages
= (9x - 3.85x) = 5.15x
Reqd. % = (5.15x / 9x) × 100 = 57.22%
Hence, option (c) is correct

2. Out of his total income, Ravi gets 40% from his job, 40% from return of investments and rest from freelancing. Out of his total income, Sunil gets 30% from his job and 25% from freelancing. If income received by Ravi from his job is Rs. 9000 more than that by Sunil and income received by Sunil from freelancing is Rs. 1500 less than that by Ravi. Find the ratio of their incomes.

Correct Answer: (a) 3:2 
Solution:

Let the total income of Ravi and Sunil be Rs. ‘x’ and Rs. y, respectively

Therefore, income of Ravi from his job = Rs. 0.4x
Income of Ravi from freelancing
= (1 − 0.4 − 0.4)x = Rs. 0.2x
Income of Sunil from his job = Rs. 0.3y
Income of Sunil from freelancing = Rs. 0.25y
According to the question,
0.4x − 0.3y = 9000 …(1)
0.2x − 0.25y = 1500 …(2)
On solving equation (1) and (2), we get
Income of Ravi = x = Rs. 45000
Income of Sunil = y = Rs. 30000
Required ratio = 45000:30000 = 3:2

3. Monthly income of A is 25% more than the monthly income of B. Monthly savings of A is 20% more than the monthly savings of B. Monthly expenditure of A is 80% more than the monthly savings of B. Find the difference between the monthly incomes of A and B if the monthly expenditure of B is Rs. 4,000 less than that of A.

Correct Answer: (b) Rs. 6,000  
Solution:

Let the monthly income of B be Rs. x
So, the monthly income of A = Rs. 1.25x
Let the monthly savings of B be Rs. y
So, the monthly savings of A = Rs. 1.2y
Monthly expenditure of A = Rs. 1.8y

Monthly expenditure of B = Rs. (1.8y - 4000)
According to question: (1.2y + 1.8y)/(y + 1.8y - 4000) = 1.25x/x
3y/(2.8y - 4000) = 5/4
12y = 14y - 20000
2y = 20000
y = 10000
So, the monthly income of A = 3 × 10000
= Rs. 30,000
Monthly income of B = 30000 × 4/5 = Rs. 24,000
So, the difference between the monthly incomes of A and B = 30000 - 24000 = Rs. 6,000

4. Directions (4-5) : Answer the questions based on the information given below.

Three friends Raman, Raghav and Ramesh, each have different monthly incomes. Monthly incomes of Raman and Raghav are in the ratio of 8:9, respectively. Monthly savings of Raman and Raghav are in the ratio 5:6, respectively. Raghav saves 50% of his monthly salary. Monthly incomes of Raman and Ramesh are in the ratio 2:3, respectively. Monthly expenditure of Raman is Rs. 1,000 less than the monthly expenditure of Raghav. Monthly expenditure of Raghav is 40% less than the monthly expenditure of Ramesh.

Ques. Find the difference between the monthly savings of Raman and Ramesh.

Correct Answer: (b) Rs. 3,000 
Solution:

Let the monthly incomes of Raman and Raghav be Rs. 8x and Rs. 9x respectively.
Monthly expenditure of Raghav
= 0.50 × 9x = Rs. 4.5x
Monthly expenditure of Raman = Rs. (4.5x - 1000)
According to question: (8x - 4.5x + 1000)/(9x - 4.5x) = 5/6
21x + 6000 = 22.5x
1.5x = 6000
x = 4000
So, the monthly incomes of Raman and Raghav are Rs. 32,000 and Rs. 36,000 respectively.
Monthly expenditure of Raghav = Monthly savings of Raghav = Rs. 18,000
Monthly expenditure of Raman
= 18000 - 1000 = Rs. 17,000
Monthly savings of Raman
= 32000 - 17000 = Rs. 15,000
Monthly salary of Ramesh = 32000 × 3/2
= Rs. 48,000
Monthly expenditure of Ramesh
= 18000/0.60 = Rs. 30,000
Monthly savings of Ramesh = 48000 - 30,000
= Rs. 18,000
So, the difference in the monthly savings of Ramesh and Raman = 18000 - 15000 = Rs. 3,000

5. Raghav invested his 50% of his monthly savings in a scheme offering 10% compound interest for three years compounded annually. Ramesh invested 40% of his monthly savings in another scheme offering 13% simple interest for three years. Find the difference between the amounts received by Raghav and Ramesh after three years.

Correct Answer: (e) None of these
Solution:

Let the monthly incomes of Raman and Raghav be Rs. 8x and Rs. 9x respectively.
Monthly expenditure of Raghav = 0.50 × 9x = Rs. 4.5x
Monthly expenditure of Raman = Rs. (4.5x - 1000)
According to question: (8x - 4.5x + 1000)/(9x - 4.5x) = 5/6
21x + 6000 = 22.5x
1.5x = 6000, x = 4000
So, the monthly incomes of Raman and Raghav are Rs. 32,000 and Rs. 36,000 respectively.
Monthly expenditure of Raghav = Monthly savings of Raghav = Rs. 18,000
Monthly expenditure of Raman = 18000 - 1000
= Rs. 17,000
Monthly savings of Raman = 32000 - 17000
= Rs. 15,000
Monthly salary of Ramesh = 32000 × 3/2
= Rs. 48,000

= Rs. 30,000
Monthly savings of Ramesh = 48000 - 30,000
= Rs. 18,000
Amount invested by Raghav = 18000 × 0.50
= Rs. 9,000
Amount received by Raghav after three years
= 9000 × (1 + 0.10)³ = 9000 × 1.331 = Rs. 11,979
Amount invested by Ramesh = 18000 × 0.40
= Rs. 7,200
Amount received by Ramesh after three years
= 7200 + 7200 × 3 × 0.13
= 7200 + 2808 = Rs. 10,008
So, the desired difference = 11979 - 10008
= Rs. 1,971

6. In a group, the ratio of number of males to that of females is 5:3. 20% of females and 80% of males, like fast foods. Out of the remaining number of people, the ratio of the persons who drink and the person who do not drink is 2:1, respectively. If the sum of the number of males who like fast food and number of people who drink out of the remaining person is 94, then find the total number of females in the group.

Correct Answer: (e) 45
Solution:Let the total number of males and females in the group be 5x and 3x respectively.
According to the question,
Number of males who like fast foods = 0.8 × 5x
= 4x
Number of females who like fast foods = 0.2 × 3x
= 0.6x
Remaining number of people = 8x - (4x + 0.6x)
= 3.4x
Number of males who drink = 3.4x × (2/3)
= 6.8x/3
Therefore, 4x + (6.8x/3) = 94
Or, 18.8x = 282
Or, x = 282/18.8 = 15
Therefore, total number of females in the group = 3x = 45

7. Directions (7-8): Answer the questions based on the information given below.

Monthly incomes of Rohit, Rajat and Ramesh are in the ratio 9:5:7, respectively. Monthly saving of Rohit is 60% more than the monthly saving of Ramesh. Monthly expenditure of Rohit is twice the monthly saving of Ramesh. Monthly expenditure of Rohit is Rs. 1,000 more than the monthly expenditure of Ramesh, while the monthly expenditure of Rajat is Rs. 3,000 less than the monthly expenditure of Ramesh.

Ques. Find the average monthly income of Rohit, Rajat and Ramesh

Correct Answer: (b) Rs. 14,000 
Solution:Let the monthly saving of Ramesh = Rs. x
So, the monthly savings of Rohit = Rs. 1.6x
Monthly expenditure of Rohit = Rs. 2x
So, the monthly expenditure of Ramesh
= Rs. 2x - 1000
According to question: (1.6x + 2x)/(x + 2x - 1000) = 9/7
3.6x/(3x - 1000) = 9/7
2.8x = 3x - 1000
0.2x = 1000
x = 5000
So, the monthly saving of Ramesh = Rs. 5,000
So, the monthly savings of Rohit
= 1.6 × 5000 = Rs. 8,000
Monthly expenditure of Rohit = 2 × 5000
= Rs. 10,000
So, the monthly expenditure of Ramesh
= 10000 - 1000 = Rs. 9,000
Monthly income of Rohit = 3.6 × 5000 = Rs. 18,000
Monthly income of Ramesh
= 18000 × 7/9 = 14,000
Monthly income of Rajat = 18000 × 5/9 = 10,000
Monthly expenditure of Rajat
= 9000 - 3000 = Rs. 6,000
So, the monthly savings of Rajat
= 10000 - 6000 = Rs. 4,000
Desired average
= (18000 + 14000 + 10000)/3 = Rs. 14,000

8. Find the monthly savings of Rajat.

Correct Answer: (a) Rs. 4,000 
Solution:Let the monthly saving of Ramesh be Rs. x
So, the monthly savings of Rohit = Rs. 1.6x
Monthly expenditure of Rohit = Rs. 2x
So, the monthly expenditure of Ramesh
= Rs. 2x - 1,000
According to question: (1.6x + 2x)/(x + 2x - 1000)
= 9/7
3.6x/(3x - 1000) = 9/7
2.8x = 3x - 1000
0.2x = 1000
x = 5000
So, the monthly saving of Ramesh = Rs. 5,000
So, the monthly savings of Rohit
= 1.6 × 5000 = Rs. 8,000
Monthly expenditure of Rohit
= 2 × 5000 = Rs. 10,000
So, the monthly expenditure of Ramesh
= 10000 - 1000 = Rs. 9,000
Monthly income of Rohit = 3.6 × 5000 = Rs. 18,000
Monthly income of Ramesh
= 18000 × 7/9 = 14,000
Monthly income of Rajat = 18000 × 5/9 = 10,000
Monthly expenditure of Rajat
= 9000 - 3000 = Rs. 6,000
So, the monthly savings of Rajat
= 10000 - 6000 = Rs. 4,000
Monthly savings of Rajat = Rs. 4,000

9. The incomes of ‘A’ and ‘C’ are in the ratio 4:3, respectively. ‘A’ and ‘C’ spend 37.5% and 75% of their respective incomes and the savings of ‘B’ is 60% of the sum of savings of ‘A’ and ‘C’. If ‘B’ saves Rs. 3,900, which is Rs. 300 more than his expense, then find the sum of incomes of ‘A’, ‘B’ and ‘C’.

Correct Answer: (a) Rs. 21,500 
Solution:Let the income of ‘A’ = Rs. ‘16y’
Then, income of ‘C’ = 16y × (3/4) = Rs. ‘12y’
Savings of ‘A’ = 16y × (1 − 0.375) = Rs. ‘10y’
Savings of ‘C’ = 12y × (1 − 0.75) = Rs. ‘3y’
Savings of ‘B’ = (10y + 3y) × 0.60 = Rs. ‘7.8y’
ATQ:
7.8y = 3900
So, y = (3900 ÷ 7.8) = 500
So, income of ‘A’ = 16 × 500 = Rs. 8,000
Income of ‘B’ = 3900 + (3900 − 300) = Rs. 7,500
Income of ‘C’ = 12 × 500 = Rs. 6,000
So, sum of incomes of ‘A’, ‘B’ and ‘C’ = 8000 + 7500 + 6000 = Rs. 21,500

10. Out of his total savings Joy invested 25% in mutual funds and 30% in gold. Out of the remaining savings, he invested 40% in bonds and deposited the rest in his savings account. If the difference between the amount invested in gold and the amount deposited in his savings account is Rs. 1,80,000, then find the total savings of Joy.

Correct Answer: (b) Rs. 60,00,000
Solution:

Let the total savings of Joy be Rs. ‘100x’
ATQ:
Amount invested in mutual funds
= 100x × 0.25 = Rs. ‘25x’
Amount invested in Gold = 100x × 0.30 = Rs. ‘30x’
Remaining savings = 100x - 25x - 30x = Rs. ‘45x’
Amount invested in bonds = 45x × 0.40 = Rs. ‘18x’
Amount deposited in savings account
= 45x - 18x = Rs. ‘27x’
ATQ:
30x - 27x = 1,80,000
Or, 3x = 180000
So, x = 60000
So, total savings of Joy = 60000 × 100
= Rs. 60,00,000