BANK & INSURANCE (PARTNERSHIP) PART 3

Total Questions: 45

1. John and Alex started a business by investing their capitals in the ratio 4:7, respectively. After 8 months John increased his investment by Rs. 1,200 while Alex decreased his investment by Rs. 800. Find the total initial investment done by John and Alex together if the profit earned by John is Rs. 10,500 out of the total profit earned by both of them at the end of 1.5 years, which is Rs. 25,250.

Correct Answer: (b) Rs. 11,000
Solution:

Let the initial investment done by John be ‘Rs. 4x’

So, initial investment done by Alex = 4x × (7/4)

= Rs. 7x

Profits sharing ratio between John and Alex

= [(4x × 8 + (4x + 1200) × 10)] : [(7x × 8 + (7x − 800) × 10)]

= (36x + 6000) : (63x − 4000)

According to the data given,

10500 : 25250 = (36x + 6000) : (99x + 2000)

42 : 101 = (36x + 6000) : (99x + 2000)

3636x + 606000 = 4158x + 84000

4158x − 3636x = 606000 − 84000

522x = 522000

So, x = 1000

So, total initial investment done by John and Alex together

= [(4 + 7) × 1000] = Rs. 11,000

2. ‘A’ and ‘B’ entered into a business by investing Rs. 3600 and Rs. 4000, respectively. After ‘x’ months, ‘A’ and ‘B’ decreased their investments by Rs. 1200 and Rs. 400, respectively and ‘C’ entered into the business investing Rs. 4800. After 7 more months, ‘B’ and ‘C’ increased their investments by Rs. 1200 and ‘A’ left the business. If at the end of 2 years, total profit earned is Rs. 76800 and ratio of profit share of ‘A’ to ‘C’ is 41:68, respectively, then find the profit share of ‘B’.

Correct Answer: (d) Rs. 33200
Solution:

According to question,

[3600 × x + 2400 × 7] : [4800 × 7 + 6000 × (24 − 7 − x)] = 41 : 68

(3600x + 16800)/(33600 + 6000(17 − x))

= 41/68

x = 9

Ratio of profit share of ‘A’, ‘B’ and ‘C’

= [3600 × 9 + 2400 × 7] : [4000 × 9 + 3600 × 7 + 4800 × 8] : [4800 × 7 + 6000 × 8]

= 41 : 83 : 68

Desired profit = (83/192) × 76800 = Rs. 33200

3. ‘A’ invested a certain amount of money for 7 months and then withdrew 1/5th of the amount and invested the remaining amount for 5 more months. ‘B’ invested the amount equal to the amount invested by ‘A’ for last 5 months of the year. ‘C’ invested an amount equal to half the amount invested by ‘B’. A, B and C made their investments for 12 months, 12 months and 5 months respectively. If the total profit received by ‘A’ is Rs. 6600, then find the profit received by ‘C’.

Correct Answer: (b) Rs. 1200
Solution:

Let the initial investment of A be Rs. 10x

So the investment of A for last 5 months = Rs. 8x

Investment of B = Rs. 8x

Investment of C = 8x/2 = Rs. 4x

Therefore, ratio of profit received by A, B and C

= (10x × 7) + (8x × 5) : (8x × 12) : (4x × 5)

= 110x : 96x : 20x

= 55 : 48 : 10

Therefore, profit received by C

= 6600 × 10/55

= Rs. 1200

4. Directions (4-6): Answer the questions based on the information given below.

Four friends, Sita, Urmila, Radhika, and Rukmani started a business together with initial investment in the ratio of 5:4:3:4 respectively. At the end of one year, Sita withdrew Rs. 2000, Urmila invested Rs. 1000 more, and the remaining two kept their investments unchanged. At the end of 2nd year, the profit ratio of Urmila and Rukmini is 9:8, respectively. At the end of 2nd year, Sita, Urmila, Radhika and Rukmani, withdrew all their investments and then made investment of Rs. 4000, Rs. 5000, Rs. 4000 and Rs. 4000, respectively for one more year. At the end of 3rd year, they share profit in the ratio of their investment and time of investment.

Question: It is decided that Sita will be given 25% of the profit for taking care of Human resource department. At the end of 3rd year, if Sita received Rs. 4200 as profit, then find the total profit earned in the business at the end of 3rd year.

Correct Answer: (c) Rs. 9600
Solution:

Let, the ratio of initial investment of Sita, Urmila, Radhika, and Rukmani be Rs. 5a, Rs. 4a, Rs. 3a and Rs. 4a respectively.

So, their investment at the end of first year (for and year) will be Rs. (5a − 2000), Rs. (4a + 1000), Rs. 3a and 4a respectively.

According to question,

(4a+4a+1000)/8a=9/8

8a + 1000 = 9a

a = 1000

So, the investment for the first year of Sita, Urmila, Radhika, and Rukmani are Rs. 5000, Rs. 4000, Rs. 3000 and 4000 respectively.

So, the investment for the 2nd year of Sita, Urmila, Radhika, and Rukmani are Rs. 3000, Rs. 5000, Rs. 3000 and 4000 respectively.

And, the investment for the 3rd year of Sita, Urmila, Radhika, and Rukmani are Rs. 4000, Rs. 5000, Rs. 4000 and Rs. 4000 respectively.

Ratio of profit share of Sita : Urmila : Radhika : Rukmani

= (5000 + 3000 + 4000) : (4000 + 5000 + 5000) : (3000 + 3000 + 4000) : (4000 + 4000 + 4000)

= 6 : 7 : 5 : 6

Let the total profit be Rs. 96x

So, the profit given to Sita for taking care of Human resource department = 0.25 × 96x

= Rs. 24x

So, remaining profit = 96x − 24x

= Rs. 72x

So, profit share of Sita in the remaining profit

= [6 / (6 + 7 + 5 + 6)] × 72x = 18x

So, total profit of Sita = 24x + 18x = Rs. 42x

According to question,

42x = 4200, x = 100

So, total required profit earned in the business at the end of 3rd year = Rs. 9600

5. Find the average of the additional amount invested by Sita and Radhika at the end of 2nd year.

Correct Answer: (b) Rs. 1000
Solution:

Let, the ratio of initial investment of Sita, Urmila, Radhika, and Rukmani be Rs. 5x, Rs. 4x, Rs. 3x and Rs. 4x respectively.

So, their investment at the end of first year will be Rs. (5x − 2000), Rs. (4x + 1000), Rs. 3x and 4x respectively.

Let, at the end of 2nd year, ratio of initial investment of Sita, Urmila, Radhika, and Rukmani be Rs. 4y, Rs. 5y, Rs. 4y and Rs. 4y respectively.

According to question,

4x + 1000 = 5y … (i)

4x = 4y … (ii)

Using both equations, we get,

x = y = 1000

So, the investment for the first year of Sita, Urmila, Radhika, and Rukmani are Rs. 5000, Rs. 4000, Rs. 3000 and 4000 respectively.

So, the investment for the 2nd year of Sita, Urmila, Radhika, and Rukmani are Rs. 3000, Rs. 5000, Rs. 3000 and 4000 respectively.

And, the investment for the 3rd year of Sita, Urmila, Radhika, and Rukmani are Rs. 4000, Rs. 5000, Rs. 4000 and Rs. 4000 respectively.

So, additional investment of Sita at the end of 2nd year

= 4000 − 3000 = Rs. 1000

So, additional investment of Radhika at the end of 2nd year

= 4000 − 3000 = Rs. 1000

Therefore, required average

= (1000 + 1000) / 2

= Rs. 1000

6. Find the profit share of Urmila at the end of 2nd year out of total profit of Rs. 12400 at the end of 2nd year.

Correct Answer: (a) Rs. 3600
Solution:

Let, the ratio of initial investment of Sita, Urmila, Radhika, and Rukmani be Rs. 5x, Rs. 4x, Rs. 3x and Rs. 4x respectively.

So, their investment at the end of first year will be Rs. (5x − 2000), Rs. (4x + 1000), Rs. 3x and 4x respectively.

Let, at the end of 2nd year, ratio of initial investment of Sita, Urmila, Radhika, and Rukmani be Rs. 4y, Rs. 5y, Rs. 4y and Rs. 4y respectively.

According to question,

4x + 1000 = 5y … (i)

4x = 4y … (ii)

Using both equations, we get,

x = y = 1000

So, the investment for the first year of Sita, Urmila, Radhika, and Rukmani are Rs. 5000, Rs. 4000, Rs. 3000 and 4000 respectively.

So, the investment for the 2nd year of Sita, Urmila, Radhika, and Rukmani are Rs. 3000, Rs. 5000, Rs. 3000 and 4000 respectively.

Ratio of profit year of Sita : Urmila : Radhika : Rukmani

= (5000 + 3000) : (4000 + 5000) : (3000 + 3000) : (4000 + 4000)

= 8 : 9 : 6 : 8

Therefore, profit share of Urmila

= [9 / (8 + 9 + 6 + 8)] × 12400

= Rs. 3600

7. Radhe invested Rs. ____ in a scheme offering compound interest of 10% p.a., compounded annually. Shyam invested Rs. 5000 more than Radhe in another scheme offering simple interest of 12% p.a. Difference between the interests earned by Radhe and Shyam after three years is Rs. ____.

The values given in which of the following options will fill the blanks in the same order in which is it given to make the above statement true:

I. 12500, 2162.5
II. 4800, 1399.2
III. 8000, 2032
IV. 12000, 2248

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

Let the amount invested by Radhe be Rs. x

So, the amount invested by Shyam = Rs. x + 5000

Interest earned by Radhe

= x × {(1 + 0.10)^3 − 1}

= Rs. 0.331x

Interest earned by Shyam

= (x + 5000) × 0.12 × 3

= 0.36x + 1800

So, the difference between the interests earned by Shyam and Radhe

= 0.36x + 1800 − 0.331x

= Rs. 0.029x + 1800

For ‘I’

Difference between the interests

= 0.029 × 12500 + 1800

= Rs. 2162.5

So, ‘I’ can be the answer.

For ‘II’

Difference between the interests

= 0.029 × 4800 + 1800 = Rs. 1939.2 ≠ 1399.2

So, ‘II’ can't be the answer.

For ‘III’

Difference between the interests

= 0.029 × 8000 + 1800

= Rs. 2032

So, ‘III’ can be the answer.

For ‘IV’

Difference between the interests

= 0.029 × 12000 + 1800

= Rs. 2148 ≠ 2248

So, ‘IV’ can't be the answer.

Hence, Only I and III option is correct.

8. A, B and C started a business with initial investments of Rs. 2,000, Rs. 2,400 and Rs. 3,000 respectively. After one year, A and B made additional investments equal to 25% and 20% of their initial investments, respectively, whereas C withdrew 10% of his initial investment. After one more year A, B and C withdrew all their investments and made small investments of Rs. ‘x + 270’, Rs. ‘x + 130’ and Rs. ‘x + 350’ respectively to maintain the business. Find the profit share of B out of the total profit of Rs. 4,350 after three years.

Correct Answer: (c) Rs. 1,450
Solution:

Investment of A for first two years

= 2000 + 2000 × 1.25 = Rs. 4,500

Investment of B for first two years
= 2400 + 2400 × 1.20 = Rs. 5,280

Investment of C for first two years
= 3000 + 3000 × 0.90 = Rs. 5,700

Ratio of profit share of A : B : C
= (4500 + x + 270) : (5280 + x + 130) : (5700 + x + 350)

= 4770 + x : 5410 + x : 6050 + x

So, the profit share of B
= ((5410 + x)/(4770 + x + 5410 + x + 6050 + x)) × 4350

= (5410 + x)/(16230 + 3x) × 4350

= 1/3 × 4350 = Rs. 1,450

9. ‘A’ and ‘B’ started a business together. ‘A’ invested for 8 months while ‘B’ invested for 10 months. Out of the total annual profit share, 20% is given to ‘A’ as he is an active partner and remaining profit is distributed between ‘A’ and ‘B’ in the ratio of their investments and total profit share received by ‘A’ and ‘B’ is equal. If the initial investment of ‘A’ is Rs. 6600, find the initial investment of ‘B’.

Correct Answer: (d) Rs. 8800
Solution:

Let the initial investment of ‘B’ = Rs. x

Let the total profit share = Rs. 100a

Profit share of ‘A’ = Rs. 50a

Profit share of ‘B’ = Rs. 50a

Profit share of ‘A’ to ‘B’
= (6600 × 8) : (x × 10)

= 5280 : x

According to the question,

50a = 20a + 80a × [5280/(5280 + x)]

30a = 80a [5280/(5280 + x)]

3/8 = 5280/(5280 + x)

15840 + 3x = 42240

3x = 26400

x = 8800

Investment of ‘B’ = Rs. 8800

10. ‘A’, ‘B’ and ‘C’ started a business where ‘B’ invested Rs. 2,000 more than ‘A’ while ‘C’ invested Rs. 500 less than 75% of the amount invested by ‘B’. ‘C’ invested for 4 months more than the time for which ‘A’ invested his capital while the time period for which ‘B’ invested was 10% less than the time for which ‘A’ invested. The profit share of ‘B’ was 65% more than that of ‘A’. Which among the following can be determined based on the above information?

I. The time period for which ‘A’ invested
II. Ratio of profit shares of ‘B’ and ‘C’ respectively
III. Average investment of ‘A’ and ‘B’ together.

Correct Answer: (a) Only III
Solution:

Let the investment of ‘A’ = Rs. ‘x’

Then investment of ‘B’ = Rs. (x + 2000)

Investment of ‘C’
= (x + 2000) × 0.75 − 500

= 0.75x + 1500 − 500

= Rs. (0.75x + 1000)

Let the time period for which ‘A’ invested be 10y months

Then time period for which ‘C’ invested
= (10y + 4) months

Time period for which ‘B’ invested
= 10y × 0.9 = 9y months

Ratio of profit shares of ‘A’ and ‘B’ respectively

= (x × 10y) : ((x + 2000) × 9y)

= 10xy : (9xy + 18000y)

According to the question,

10xy × 1.65 = 9xy + 18000y

16.5xy = 9xy + 18000y

7.5xy = 18000y

So, x = 18000 ÷ 7.5 = 2400

So, investments of ‘A’, ‘B’ and ‘C’ are
Rs. 2,400, Rs. 4,400 and Rs. 2,800, respectively

So, ratio of profit shares of ‘A’ and ‘B’
= 24000y : 39600y

We have, 39600y = 24000y × 1.65

So, the value of ‘y’ cannot be determined.

For I:
Since, the value of ‘y’ cannot be determined, the time period of investment of ‘A’ also cannot be determined.
So, statement I cannot be determined.

For II:
Ratio of profit shares of ‘B’ and ‘C’ respectively

= (4400 × 9y) : (2800 × (10y + 4))

= 39600y : (28000y + 11200)

Since, the value of ‘y’ cannot be determined, the ratio of profit shares of ‘B’ and ‘C’ also cannot be determined.

So, statement II cannot be determined.

For III:
Average investment of ‘A’ and ‘B’
= (2400 + 4400) ÷ 2 = Rs. 3,400

So, statement III can be determined.