BANK & INSURANCE (PARTNERSHIP) PART 3

Total Questions: 45

11. Directions (11-13): Answer the questions based on the information given below.

‘A’, ‘B’ and ‘C’ started a business, in the beginning of 2018, where ‘C’ invested Rs. 8,000 while ‘A’ and ‘B’, invested in the ratio 2:3, respectively. One year later, ‘A’ increased his investment by 50% and ‘D’ joined them by investing an amount that was 150% more than the initial investment of ‘C’. After one more year, ‘E’ joined the business by investing the same amount that ‘A’ and ‘B’ together had invested initially and ‘B’ and ‘C’ increased their investments by 20% and 25%, respectively. One more year later, ‘B’ increased his investment by Rs. 4,000 whereas ‘C’ withdrew Rs. 1,000. At the end of 2021, the ratio of profit received by ‘A’, ‘B’, ‘C’, ‘D’ and ‘E’ in the ratio 11:14:7:12:10, respectively.

Ques. Find the difference between the amount invested by ‘E’ and ‘D’, initially.

Correct Answer: (c) Rs. 5,000
Solution:

Let the amount invested by ‘A’ and ‘B’, in 2018, be
Rs. 2x and Rs. 3x, respectively.

Additional investment by ‘A’ in 2019 = 2x × 0.5

= Rs. ‘x’

So, total investment made by ‘A’ in 2019 = 2x + x

= Rs. 3x

And, amount invested by ‘D’ = 8000 × 2.5

= Rs. 20,000

Amount invested by ‘E’ in 2020 = 2x + 3x

= Rs. 5x

Investment of ‘B’ in 2020 = 3x × 1.2

= Rs. 3.6x

Investment of ‘C’ in 2020 = 8000 × 1.25

= Rs. 10,000

Investment of ‘B’ in 2021
= Rs. (3.6x + 4000)

Investment of ‘C’ in 2021
= 10000 − 1000

= Rs. 9,000

So, ratio of profit shares of ‘A’, ‘B’, ‘C’, ‘D’ and ‘E’ at the end of 2021

= {2x + 3x × 3} : {3x × 2 + 3.6x + 3.6x + 4000} : {8000 × 2 + 10000 + 9000} : {20000 × 3} : {5x × 2}

= (11x) : (13.2x + 4000) : 35000 : 60000 : (10x)

ATQ:

{60000/(10x)} = (12/10)

So, x = 5000

So, initial investment made by ‘A’ = 2 × 5000
= Rs. 10,000

Initial investment made by ‘B’ = 3 × 5000
= Rs. 15,000

And, amount invested by ‘E’ = 10000 + 15000
= Rs. 25,000

Amount invested by ‘E’ = 5x = 5 × 5000
= Rs. 25,000

So, required difference
= 25000 − 20000

= Rs. 5,000

12. ‘A’ works as manager in the business and hence is entitled to receive a salary of 5% out of total profit. If at the end of 2021, the difference between total amount received by ‘A’ and ‘C’ is Rs. 1,23,500, then find the amount received by ‘D’ as his profit share.

Correct Answer: (d) Rs. 2,16,600
Solution:

Let the amount invested by ‘A’ and ‘B’, in 2018, be

Rs. 2x and Rs. 3x, respectively.

Additional investment by ‘A’ in 2019 = 2x × 0.5

= Rs. ‘x’

So, total investment made by ‘A’ in 2019 = 2x + x

= Rs. 3x

And, amount invested by ‘D’ = 8000 × 2.5

= Rs. 20,000

Amount invested by ‘E’ in 2020 = 2x + 3x

= Rs. 5x

Investment of ‘B’ in 2020 = 3x × 1.2

= Rs. 3.6x

Investment of ‘C’ in 2020 = 8000 × 1.25

= Rs. 10,000

Investment of ‘B’ in 2021 = Rs. (3.6x + 4000)

Investment of ‘C’ in 2021 = 10000 − 1000

= Rs. 9,000

So, ratio of profit shares of 'A', 'B', 'C', 'D' and 'E' at the end of 2021 =
{(2x + 3x × 3)} : {3x × 2 + 3.6x + 3.6x + 4000} : {8000 × 2 + 10000 + 9000} : {20000 × 3} : {5x × 2}
= (11x) : (13.2x + 4000) : 35000 : 60000 : (10x)

ATQ:
{60000/(10x)} = (12/10)

So, x = 5000

So, initial investment made by 'A' = 2 X 5000
= Rs. 10,000

Initial investment made by 'B' = 3 X 5000
= Rs. 15,000

And, amount invested by 'E' = 10000 + 15000
= Rs. 25,000

Let the total profit earned from the business be Rs. '100x'

So, salary of 'A' = 100x × 0.05 = Rs. '5x'

Remaining profit = 100x − 5x = Rs. '95x'

Profit share of 'A' = 95x × (11/54)
= Rs. (1045x/54)

Total amount received by 'A' = 5x + (1045x/54)
= Rs. {(1315x)/54}

Profit share of 'C' = 95x × (7/54) = Rs. (665x/54)

ATQ
(1315x/54) − (665x/54) = 123500

650x = 123500 × 54

x = 10260

Total profit earned from the business = 100 × 10260 = Rs. 10,26,000

So, profit share of 'D' = 1026000 × 0.95 × (12/54)
= Rs. 2,16,600

13. If ‘D’ invested Rs. (2x + 30000) at simple interest of 20% p.a. for 2 years, then find the total interest earned by ‘D’.

Correct Answer: (b) Rs. 16,000
Solution:

Let the amount invested by 'A' and 'B', in 2018, be

Rs. 2x and Rs. 3x, respectively.

Additional investment by 'A' in 2019 = 2x × 0.5
= Rs. 'x'

So, total investment made by 'A' in 2019 = 2x + x
= Rs. '3x'

And, amount invested by 'D' = 8000 × 2.5
= Rs. 20,000

Amount invested by 'E' in 2020 = 2x + 3x = Rs. '5x'

Investment of 'B' in 2020 = 3x × 1.2 = Rs. 3.6x

Investment of 'C' in 2020 = 8000 × 1.25 = Rs. 10,000

Investment of 'B' in 2021 = Rs. (3.6x + 4000)

Investment of 'C' in 2021 = 10000 − 1000 = Rs. 9,000

So, ratio of profit shares of 'A', 'B', 'C', 'D' and 'E' at the end of 2021
= {(2x + 3x × 3)} : {3x × 2 + 3.6x + 3.6x + 4000} : {8000 × 2 + 10000 + 9000} : {20000 × 3} : {5x × 2}
= (11x) : (13.2x + 4000) : 35000 : 60000 : (10x)

ATQ
{60000/(10x)} = (12/10)

So, x = 5000

So, initial investment made by 'A' = 2 X 5000
= Rs. 10,000

Initial investment made by 'B' = 3 X 5000
= Rs. 15,000

And, amount invested by ‘E’ = 10000 + 15000
= Rs. 25,000

2x + 30000 = 2 x 5000 + 30000 = Rs. 40,000

So, interest earned by ‘D’ = (40000 X 20 X 2) ÷ 100
= Rs. 16,000

14. Directions (14-15): Answer the questions based on the information given below.

‘A’ and ‘B’ started a business in the beginning of 2020 by investing Rs. ‘x’ and Rs. ‘y’, respectively. At the end of first year, ‘A’ used 60% of the profit he had earned to buy some real estate, the value of which increases at a constant rate of 8% p.a. whereas ‘B’ invested 40% of his profit share in mutual funds which grew by 15% and 20%, respectively, during the first 2 years. At the end of 2022, the value of mutual funds of ‘B’ was Rs. 16,560 and the value of real estate bought by ‘A’ was Rs. 34,992. Also (x + y) = 80,000.

Ques. Find the difference between initial investments of ‘A’ and ‘B’.

Correct Answer: (c) Rs. 20,000
Solution:

Since, x + y = 80000

So, (80000 − y) = x .......... (I)

Amount invested by 'B' in shares = 16560 ÷ 1.15 ÷ 1.2 = Rs. 12,000

So, profit earned by 'B' = 12000 ÷ 0.4 = Rs. 30,000

Amount invested by 'A' in real estate = 34992 ÷ (1.08)² = Rs. 30,000

So, profit earned by 'A' = 30000 ÷ 0.6 = Rs. 50,000

So, ratio of profit shares of 'A' and 'B' at the end of first year = (80000 − y) : y

ATQ
((80000 − y)/y) = (50000/30000)

3 × (80000 − y) = 5y

240000 − 3y = 5y

8y = 240000

So, y = 30000

So, x = 80000 − 30000 = Rs. 50,000

So, investment of 'A' = Rs. 50,000 and investment of 'B' = Rs. 30,000

Required difference = 50,000 − 30,000
= Rs. 20,000

15. Find the ratio of profit shares of ‘A’ and ‘B’, at the end of 2020.

Correct Answer: (a) 5 : 3
Solution:

Since, x + y = 80000

So, (80000 − y) = x .......... (I)

Amount invested by 'B' in shares = 16560 ÷ 1.15 ÷ 1.2 = Rs. 12,000

So, profit earned by 'B' = 12000 ÷ 0.4 = Rs. 30,000

Amount invested by 'A' in real estate = 34992 ÷ (1.08)² = Rs. 30,000

So, profit earned by 'A' = 30000 ÷ 0.6 = Rs. 50,000

So, ratio of profit shares of 'A' and 'B' at the end of first year = (80000 − y) : y

ATQ
((80000 − y)/y) = (50000/30000)

3 × (80000 − y) = 5y

240000 − 3y = 5y

8y = 240000

So, y = 30000

So, x = 80000 − 30000 = Rs. 50,000

So, investment of 'A' = Rs. 50,000 and investment of 'B' = Rs. 30,000

Required ratio = 50000 : 30000 = 5 : 3

16. ‘P’, ‘Q’ and ‘R’ entered into a partnership with the initial capital of Rs. (X + 2000), Rs. (X + 10000) and Rs. 28000, respectively. After three months, ‘P’ withdrew (2/3)rd of his initial capital, ‘Q’ withdrew half of his initial capital and ‘R’ invested Rs. 4000 more. ‘Q’ being active partner gets 20% of the total profit as extra amount and rest profit is shared among them in the ratio of their investment. If the annual profit share of ‘R’ is Rs. 13950 and total annual profit earned is Rs. 40500, then find the value of ‘X’.

Correct Answer: (b) 30000
Solution:

Profit share ratio of 'P', 'Q' and 'R', respectively =

[3(X + 2000) + 9(X + 2000)/3] : [3(X + 1000) + 9(X + 1000)/2] : [(28000 × 3) + (32000 × 9)]

= (3X + 6000 + 3X + 6000) : (3X + 3000 + 4.5X + 45000) : (84000 + 288000)

= (6X + 12000) : (7.5X + 75000) : 372000

Total profit share = Rs. 40500

Extra profit share of Q = 40500 × 20% = Rs. 8100

Remaining profit share = 40500 − 8100 = Rs. 32400

Profit share of 'R' = 372000/(6x + 12000 + 7.5x + 75000 + 372000)

13950/32400 = 372000/(13.5X + 459000)

155/360 = 124000/(4.5X + 153000)

31/72 = 124000/(4.5X + 153000)

31(4.5X + 153000) = 72 × 124000

31(0.5X + 17000) = 8 × 124000

0.5X + 17000 = 8 × 4000

0.5X = 32000 − 17000

X = 15000/0.5

X = 30000

17. ‘A’, ‘B’ and ‘C’ started a business making initial investments in the ratio of 12:13:27 respectively. After 1 year, ‘A’ added Rs. 720 more, ‘B’ added Rs. 580 more while ‘C’ added Rs. 1404 more. If total profit earned at the end of 2 years is Rs. 16224, then find profit share of ‘C’.

Correct Answer: (d) Rs. 8424
Solution:

Let initial investment made by 'A', 'B' and 'C' is Rs.

12x, Rs. 13x and Rs. 27x respectively.

Ratio of profit share of 'A', 'B' and 'C' =
[12x × 2 + 720] : [13x × 2 + 580] : [27x × 2 + 1404]
= (24x + 720) : (26x + 580) : (54x + 1404)

Profit share of 'C' =
{(54x + 1404)/(104x + 2704)} × 16224

= {54(x + 26)/104(x + 26)} × 16224

= 27/52 × 16224

= Rs. 8424

18. Directions (18-20): Answer the questions based on the information given below.

In 2008, A and B started a business together where the investment of A is three times the investment of B. After few months, C joined them with an investment equal to the half of the investment of A. After a year, B received a profit of Rs. 10000 out of total profit of Rs. 50000.

In 2009, A made additional investment of Rs. 4000 whereas B and C doubled their investment. After a year, they received total profit equal to five times of profit received by C in 2008, and profit share of B out of total profit is Rs. 12000 in 2009.

Ques. Find the ratio of investment of A in 2008 to the investment of A in 2009.

Correct Answer: (e) 9:10
Solution:

Let, investment of B in 2008 be Rs. x

So, investment of A in 2008 = Rs. 3x

Let, C joined after ‘y’ months after starting of business in 2008.

So, investment of C in 2008 = Rs. 1.5x

So, ratio of share of profit in 2008:

A : B : C = (3x × 12) : (x × 12) : [1.5x × (12 − y)]

= 24 : 8 : (12 − y)

According to question,

8/[24 + 8 + (12 − y)] = 10000/50000

8/(32 + 12 − y) = 1/5

40 = 44 − y

y = 44 − 40

y = 4 months

So, ratio of share of profit in 2008:
A : B : C = 24 : 8 : 8 = 3 : 1 : 1

Share of C in 2008 = (1/5) × 50000 = Rs. 10000

Let, investment of B in 2009 = Rs. 2x

So, investment of A in 2009 = Rs. (3x + 4000)

So, investment of C in 2009 = Rs. 3x

So, total profit received by them in 2009
= 5 × 10000 = Rs. 50000

According to question,

2x/(3x + 4000 + 2x + 3x) = 12000/50000

2x/(8x + 4000) = 6/25

50x = 48x + 24000

2x = 24000

x = 24000/2 = 12000

Therefore, investment of A in 2008
= 3 × 12000 = Rs. 36000

Therefore, investment of A in 2009
= (36000 + 4000) = Rs. 40000

Therefore, required ratio = 36000 : 40000 = 9 : 10

19. Find the difference between profit share of C in 2009 and profit share of C in 2008.

Correct Answer: (c) Rs. 8000
Solution:

Let, investment of B in 2008 be Rs. x

So, investment of A in 2008 = Rs. 3x

Let, C joined after y months after start of business in 2008.

So, investment of C in 2008 = Rs. 1.5x

So, ratio of share of profit in 2008:

A : B : C = (3x × 12) : (x × 12) : [1.5x × (12 − y)]

= 24 : 8 : (12 − y)

According to question,

8/[24 + 8 + (12 − y)] = 10000/50000

8/(32 + 12 − y) = 1/5

40 = 44 − y

y = 44 − 40

y = 4 months

So, ratio of share of profit in 2008:
A : B : C = 24 : 8 : 8 = 3 : 1 : 1

Share of C in 2008 = (1/5) × 50000 = Rs. 10000

Let, investment of B in 2009 = Rs. 2x

So, investment of A in 2009 = Rs. (3x + 4000)

So, investment of C in 2009 = Rs. 3x

So, total profit received by them in 2009
= 5 × 10000 = Rs. 50000

According to question,

2x/(3x + 4000 + 2x + 3x) = 12000/50000

2x/(8x + 4000) = 6/25

50x = 48x + 24000

2x = 24000

x = 24000/2 = 12000

Therefore, investment of B in 2009 =
2 × 12000 = Rs. 24000

Therefore, investment of A in 2009 =
(36000 + 4000) = Rs. 40000

Therefore, investment of C in 2009 =
3 × 12000 = Rs. 36000

So, ratio of profit share in 2009
A : B : C = 40000 : 24000 : 36000 = 10 : 6 : 9

Therefore, profit share of C in 2009

= [9/(10 + 6 + 9)] × 50000

= Rs. 18000

Therefore, required difference

= 18000 − 10000

= Rs. 8000

20. Find the average of profit share of A in 2008 and profit share of A in 2009 taken together.

Correct Answer: (b) Rs. 25000
Solution:

Let, investment of B in 2008 be Rs. x

So, investment of A in 2008 = Rs. 3x

Let, C joined after y months after start of business in 2008.

So, investment of C in 2008 = Rs. 1.5x

So, ratio of share of profit in 2008:

A : B : C = (3x × 12) : (x × 12) : [1.5x × (12 − y)]

= 24 : 8 : (12 − y)

According to question,

8/[24 + 8 + (12 − y)] = 10000/50000

8/(32 + 12 − y) = 1/5

40 = 44 − y

y = 44 − 40

y = 4 months

So, ratio of share of profit in 2008:
A : B : C = 24 : 8 : 8 = 3 : 1 : 1

Therefore, share of A in 2008

= (3/5) × 50000

= Rs. 30000

Let, investment of B in 2009 = Rs. 2x

So, investment of A in 2009 = Rs. (3x + 4000)

So, investment of C in 2009 = Rs. 3x

So, total profit received by them in 2009

= 5 × 10000 = Rs. 50000

According to question,

2x/(3x + 4000 + 2x + 3x) = 12000/50000

2x/(8x + 4000) = 6/25
50x = 48x + 24000
2x = 24000, x = 24000/2 = 12000

Therefore, investment of B in 2009 = 2 × 12000
= Rs. 24000

Therefore, investment of A in 2009
= Rs. (36000 + 4000) = Rs. 40000

Therefore, investment of C in 2009 = 3 × 12000
= Rs. 36000

So, ratio of profit share in 2009
A:B:C = 40000:24000:36000 = 10:6:9

Therefore, profit share of A in 2009
= [10/(10 + 6 + 9)] × 50000 = Rs. 20000

Therefore, required average = (30000 + 20000)/2
= Rs. 25000