BANK & INSURANCE (PARTNERSHIP) PART 3

Total Questions: 45

21. Directions (21-22): Answer the questions based on information given below.

‘A’, ‘B’ and ‘C’ started a business together by investing a total amount of Rs. 6000. After 6 months from the beginning of the partnership, ‘A’ added Rs. 800 more and ‘C’ added Rs. 1000 more. After 8 more months, ‘B’ withdrew Rs. 200 and withdrew Rs. 200 and ‘C’ left. At the end of the partnership, profit received by ‘C’ is (9/7) times of the profit received by ‘B’. ‘B’ invested for 4 more months more than ‘C’ and initial investment made by ‘B’ is Rs. 400 less than that by ‘C’.

Ques. If total profit earned by all of them together at the end of the partnership is Rs. 417600, then find the profit share of ‘A’.

Correct Answer: (b) Rs. 187200
Solution:

Let total time for which ‘A’ and ‘B’ made their investment be ‘t’ months.

Let initial investment made by ‘A’ and ‘B’ be Rs. ‘x’ and Rs. ‘y’ respectively.

So, initial investment made by ‘C’ = Rs. (6000 − x − y)

Total investment made by ‘A’
= x × 6 + (x + 800) × 8 + (x + 800 − 200) × (t − 14)

= Rs. (xt + 600t − 2000)

Total investment made by ‘B’
= y × 14 + (y − 200) × (t − 14)

= Rs. (yt − 200t + 2800)

Total investment made by ‘C’
= (6000 − x − y) × 6 + (6000 − x − y + 1000) × 8

= Rs. (92000 − 14x − 14y)

And, y + 400 = 6000 − x − y

So, 2y = 5600 − x

Or, x = 5600 − 2y ............ (1)

And, t = 8 + 6 + 4 = 18

So, ratio of profit share of ‘A’, ‘B’ and ‘C’, respectively

= [(5600 − 2y) × 18 + 600 × 18 − 2000] : [y × 18 − 200 × 18 + 2800] : [92000 − 14x (5600 − 2y) − 14y]

So, [(y × 18 − 200 × 18 + 2800)] : [92000 − 14x (5600 − 2y) − 14y] = 7 : 9

Solving above equation, we get

y = 1600

So, x = 5600 − 2 × 1600 = 2400

So, ratio of profit shares of ‘A’, ‘B’ and ‘C’, respectively

= 52000 : 28000 : 36000 = 13 : 7 : 9

Profit share of ‘A’ = (13/29) × 417600
= Rs. 187200

22. Initial investment made by ‘C’ is:

Correct Answer: (c) Rs. 2000
Solution:

Let total time for which ‘A’ and ‘B’ made their investment be ‘t’ months.

Let initial investment made by ‘A’ and ‘B’ be Rs. ‘x’ and Rs. ‘y’, respectively.

So, initial investment made by ‘C’
= Rs. (6000 − x − y)

Total investment made by ‘A’
= x × 6 + (x + 800) × 8 + (x + 800 − 200) × (t − 14)

= Rs. (xt + 600t − 2000)

Total investment made by ‘B’
= y × 14 + (y − 200) × (t − 14)

= Rs. (yt − 200t + 2800)

Total investment made by ‘C’
= (6000 − x − y) × 6 + (6000 − x − y + 1000) × 8

= Rs. (92000 − 14x − 14y)

And, y + 400 = 6000 − x − y

So, 2y = 5600 − x

Or, x = 5600 − 2y ............ (1)

And, t = 8 + 6 + 4 = 18

So, ratio of profit share of ‘A’, ‘B’ and ‘C’, respectively

= [(5600 − 2y) × 18 + 600 × 18 − 2000] : [y × 18 − 200 × 18 + 2800] : [92000 − 14x (5600 − 2y) − 14y]

So, [(y × 18 − 200 × 18 + 2800)] : [92000 − 14x (5600 − 2y) − 14y] = 7 : 9

Solving above equation, we get

y = 1600

So, x = 5600 − 2 × 1600 = 2400

So, ratio of profit shares of ‘A’, ‘B’ and ‘C’, respectively

= 52000 : 28000 : 36000 = 13 : 7 : 9

Initial investment made by ‘C’ = Rs. 2000

23. Hema, Jaya, and Sushma together started a business with investments of Rs. ‘x’, Rs. ‘x + 600’ and Rs. ‘x − 400’, respectively. After a year, Hema and Jaya increased their investments by 10% and 20%, respectively while Sushma decreased her investment by 10%. If the total investment done by Hema and Jaya together in the second year was Rs. 3480, and the total profit earned after 2 years was Rs. 6000, then which of the following statement(s) is/are true?

I. 80% of ‘x’ is 960.
II. Profit share of Hema at the end of 2 years was Rs. 1890
III. If Sushma invested the profit share received by her at the end of 2 years at simple interest of 35% p.a. for 80 months then total interest received by her would be Rs. 2660.

Correct Answer: (e) All I, II and III
Solution:

Total investment done by Hema till the second year

= 1.1x

Total investment done by Jaya till the second year
= 1.2 × (x + 600) = Rs. 1.2x + 720

So, 1.1x + 1.2x + 720 = 3480

Or, 2.3x = 2760

Or, x = 1200

Ratio of profit share of Hema, Jaya and Sushma respectively after 2 years

= (2.1 × 1200) : (2.2 × 1800) : (1.9 × 800)

= 2520 : 3960 : 1520

= 63 : 99 : 38

For ‘I’:

80% of ‘x’ = 0.80 × 1200 = 960

So, ‘I’ can be the answer.

For ‘II’:

Share of profit of Hema
= (63/200) × 6000

= Rs. 1890

So, ‘II’ can be the answer.

For ‘III’:

Profit share of Sushma
= (38/200) × 6000

= Rs. 1140

Desired interest = 1140 × (20/3) × 0.35

= Rs. 2660

So, ‘III’ can be the answer.

24. Directions (24-26): Answer the questions based on the information given below.

A, B and C started a business with certain initial investments. After one year, additional investments were done by A and B in the ratio of 3:5 respectively. Additional investment by C after one year is 40% more than the additional investment of B after one year. In the third year, A, B and C withdrew 20%, 25% and 1/3rd respectively of the investments made by each of them in the previous year.

Ques. If initial investments of A, B and C were Rs. 12,000, Rs. 9,000 and Rs. 6,000 respectively. After two years, a profit of Rs. 7,050 is generated, which is distributed among them in the ratio of their investments. Find the profit share of B.

Correct Answer: (d) Rs. 2,350
Solution:

Let the additional investments of A and B after one year be Rs. 3x and Rs. 5x respectively.

Additional investment of C after one year
= 1.4 × 5x = Rs. 7x

Respective ratio of profits of A, B and C after 2 years

= 12000 + 12000 + 3x : 9000 + 9000 + 5x : 6000 + 6000 + 7x

= 24000 + 3x : 18000 + 5x : 12000 + 7x

So, the profit share of B

= {(18000 + 5x)/(54000 + 15x)} × 7050

= (1/3) × 7050

= Rs. 2,350

25. If initial investment of A is four times his additional investment, initial investment of B is 120% more than his additional investment and additional investment of C is 65% less than his initial investment and after three years, a profit of Rs. 7040 is generated, it is distributed among them in the ratio of their investments. Find the profit share of C after three years.

Correct Answer: (b) Rs. 3200
Solution:

Let the additional investments of A and B after one year be Rs. 3x and Rs. 5x respectively.

So, the additional investment of C after one year
= 1.40 × 5x = Rs. 7x

Initial investment of A = 4 × 3x = Rs. 12x

Initial investment of B = 2.20 × 5x = Rs. 11x

Initial investment of C = 7x/0.35 = Rs. 20x

Total investment made by A in two years

= 3x + 12x = Rs. 15x

Total investment made by B in two years = 5x + 11x = Rs. 16x

Total investment made by C in two years = 7x + 20x
= Rs. 27x

Investment of A for the third year = 15x × 0.80
= Rs. 12x

Investment of B for the third year = 16x × 0.75
= Rs. 12x

Investment of C for the third year = 27x × 2/3
= Rs. 18x

Respective ratio of profits of A, B and C
= (12x + 15x + 12x) : (11x + 16x + 12x) : (20x + 27x + 18x)

= 39x : 39x : 65x

= 3 : 3 : 5

So, the profit share of C
= (5/11) × 7040 = Rs. 3200

26. If initial investments of A, B and C were Rs. 1575, Rs. 1875 and Rs. 2025 respectively and the profit share of A, out of the total profit of 5,280 after two years is Rs. 1,440, then find the difference between the additional investments of B and C in the 2nd year.

Correct Answer: (a) Rs. 300
Solution:

Let the additional investments of A and B after one year be Rs. 3x and Rs. 5x respectively.

So, the additional investment of C after one year
= 1.40 × 5x = Rs. 7x

Respective ratio of profits of A, B and C

= 1575 + 1575 + 3x : 1875 + 1875 + 5x : 2025 + 2025 + 7x

= 3150 + 3x : 3750 + 5x : 4050 + 7x

According to question

(3150 + 3x) / (10950 + 15x) = 1440 / 5280

(3150 + 3x) / (10950 + 15x) = 3 / 11

34650 + 33x = 32850 + 45x

12x = 1800

x = 150

So, the additional investments of A, B and C are
Rs. 450, Rs. 750 and Rs. 1050

So, the difference between the additional investments of B and C
= 1050 − 750 = Rs. 300

27. Directions (27-29): Answer the questions based on the information given below.

‘A’ and ‘B’ started a business by investing Rs. (x + 12000) and (2x − 6000), respectively. After 3 months, ‘A’ withdrew Rs. 6000 and ‘B’ added Rs. 6000 to his initial investment and ‘C’ joined with an investment which is Rs. 6000 more than the sum of initial investment made by ‘A’ and ‘B’. After 1 year from starting, ‘C’ withdrew Rs. 12000 from his initial investment and ‘A’ and ‘B’ left. After 15 months from starting, ‘C’ received a profit of Rs. 13500 out of total profit of Rs. 26100. ‘P’ invested Rs. (1.5x – y) at compound interest at the rate of 20% p.a. compounded annually and received an amount equal to Rs. (2x – 2400) at the end of two years.

Ques. Find the value of (x – y).

Correct Answer: (a) 9000
Solution:

Ratio of the profit received by ‘A’, ‘B’ and ‘C’

{(x + 12000) × 3 + (x + 12000 − 6000) × 9} :
{(2x − 6000) × 3 + (2x − 6000 + 6000) × 9} :
{(3x + 12000 − 12000) × 3}

= (4x + 30000) : (8x − 6000) : (12x + 36000)

According to the question,

{(12x + 36000) / (4x + 30000 + 8x − 6000 + 12x + 36000)}
= 13500 / 26100

29 × (12x + 36000) = 15 × (24x + 60000)

348x + 1044000 = 360x + 900000

12x = 144000

x = 12000

Therefore, sum invested by ‘P’ = (1.5x − y)
= Rs. (18000 − y)

According to the question,

(18000 − y)(1 + 20/100)² = 2 × 12000 − 24000

25920 − 1.44y = 21600

1.44y = 4320

y = 3000

Required value = 12000 − 3000 = 9000

28. The interest received by ‘P’ is equal to

I. Rs. (0.5x + 600)
II. Rs. (3y – 2400)
III. Rs. (x – 2y + 300)

Correct Answer: (d) Only I and II
Solution:

Ratio of the profit received by ‘A’, ‘B’ and ‘C’

{(x + 12000) × 3 + (x + 12000 − 6000) × 9} : {(2x − 6000) × 3 + (2x − 6000 + 6000) × 9} : {(3x + 12000 − 12000) × 3}

= (4x + 30000) : (8x − 6000) : (12x + 36000)

According to the question,

{(12x + 36000) / (4x + 30000 + 8x − 6000 + 12x + 36000)}
= 13500 / 26100

29 × (12x + 36000) = 15 × (24x + 60000)

348x + 1044000 = 360x + 900000

12x = 144000

x = 12000

Therefore, sum invested by ‘P’ = (1.5x − y)
= Rs. (18000 − y)

According to the question,

(18000 − y)(1 + 20/100)² = 2 × 12000 − 24000

25920 − 1.44y = 21600

1.44y = 4320

y = 3000

Interest received by ‘P’
= 0.44 × (1.5x − y)

= 0.44 × 15000 = Rs. 6600

For I:

0.5x + 600 = 0.5 × 12000 + 600 = Rs. 6600

Therefore, I is true.

For II:

3y − 2400 = 3 × 3000 − 2400 = Rs. 6600

Therefore, II is true.

For III:

x − 2y + 300 = 12000 − 2 × 3000 + 300

= Rs. 6300

Therefore, III is false.

29. Find the difference between the profit received by ‘A’ and ‘B’.

Correct Answer: (b) Rs. 900
Solution:

Ratio of the profit received by ‘A’, ‘B’ and ‘C’

{(x + 12000) × 3 + (x + 12000 − 6000) × 9} :
{(2x − 6000) × 3 + (2x − 6000 + 6000) × 9} :
{(3x + 12000 − 12000) × 3}

= (4x + 30000) : (8x − 6000) : (12x + 36000)

According to the question,

{(12x + 36000) / (4x + 30000 + 8x − 6000 + 12x + 36000)}
= 13500 / 26100

29 × (12x + 36000) = 15 × (24x + 60000)

348x + 1044000 = 360x + 900000

12x = 144000

x = 12000

Therefore, sum invested by ‘P’ = (1.5x − y)
= Rs. (18000 − y)

According to the question,

(18000 − y)(1 + 20/100)² = 2 × 12000 − 24000

25920 − 1.44y = 21600

1.44y = 4320

y = 3000

Profit received by ‘A’
= (26100/58) × 13

= Rs. 5850

Profit received by ‘B’
= (26100/58) × 15

= Rs. 6750

Required difference
= 6750 − 5850 = Rs. 900

30. Pollard and Bravo entered into a business by investing Rs. 3000 and Rs. 5000 respectively. After 1 year, Pollard added ____ more and Bravo withdrew Rs. 1000 respectively. After two years, profit share of Pollard is Rs. ____ out of total profit of Rs. 15840.

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:

A. Rs. 1000, Rs. 6930
B. Rs. 1500, Rs. 7200
C. Rs. 3000, Rs. 7440
D. Rs. 1200, Rs. 7040

Correct Answer: (d) Only A, B and D
Solution:

Let additional investment made by pollard is Rs. x.

Profit share of Pollard after 2 years be Rs. y.

Ratio of profit share of Pollard to Bravo

= [3000 × 1 + (3000 + x) × 1] : [5000 × 1 + (4000 × 1)]

= (x + 6000) : (9000)

So, (x + 6000)/(x + 15000) = y/15840

For A:

x = 1000

7000/16000 = y/15840

y = 7/16 × 15840 = 6930

So, A can be the answer.

For B:
x = 1500
7500/16500 = y/15840
y = 5/11 × 15840 = 7200
So, B can be the answer.

For C:
x = 3000
9000/18000 = y/15840
y = 1/2 × 15840 = 7920
So, C cannot be the answer.

For D:
x = 1200
7200/16200 = y/15840
y = 4/9 × 15840 = 7040
So, D can be the answer.