BANK & INSURANCE (PARTNERSHIP) PART 2

Total Questions: 45

21. A, B and C are invested their amount in a business. Their capitals are respectively, Rs 15000, Rs 18000 and Rs x. A gets 24% of the total profit for managing the business. The remaining profit is divided among three in the ratio of their capitals. At the end of the year, the total profit is Rs 12000. If profit earned by A is Rs 5280, then what is the value of x?

Correct Answer: (a) Rs 24000
Solution:

The ratio of their share = 15000 : 18000 : x

Share of A = 5280

24% of the 12000 + (15000/(15000+18000+x)) × 76% of 12000 = 5280

15000/(33000+x) × 9120 = 5280 − 2880

15000/(33000+x) × 9120 = 2400

15000 × 9120 = 2400(33000 + x)

33000 + x = 57000

x = 24000

22. Three men A, B and C start a business together. They invest Rs. 15000, Rs. 12000 and Rs. 16000 respectively in the beginning. After 4 months B took out Rs. 4000 and C took out Rs. 6000. They get a profit of Rs. 54500 at the end of the year. B's share in the profit is?

Correct Answer: (b) Rs. 14000
Solution:

Ratio of profit = Ratio of capital invested

= 15000 × 12 : (4 × 12000 + 8 × 8000) : (4 × 16000 + 8 × 10000)

= 180000 : 112000 : 144000

= 90 : 56 : 72

= 45 : 28 : 36

B’s share in profit = (28 × 54500) / 109 = Rs. 14000

23. 'A' and 'B' together started a business where 'B' invested Rs. 200 more than 'A'. 6 months later, 'A' increased his investment by 50%. Out of the total annual profit of Rs. 2,900, if the profit share of 'A' was Rs. 100 more than that of 'B', then find the investment made by 'A', initially.

Correct Answer: (d) Rs. 1,200
Solution:

Let the amount invested by ‘A’, initially = Rs. ‘Y’

Then, amount invested by ‘B’, initially = Rs. (Y + 200)

Let the annual profit share of ‘B’ = Rs. ‘K’

Then, annual profit share of ‘A’ = Rs. (K + 100)

According to the question,

K + K + 100 = 2900

2K + 100 = 2900

So, K = (2900 − 100) ÷ 2 = 1400

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

= (1400 + 100) : (1400) = 15 : 14

Also, ratio of profit shares of ‘A’ and ‘B’ respectively

= (Y × 6 + Y × 1.5 × 6) : ((Y + 200) × 12)

So, (15Y) : (12Y + 2400) = (15 : 14)

210Y = 180Y + 36000

So, Y = 36000 ÷ 30 = 1200

24. ‘A’ and ‘B’ started a business by investing Rs. 12,000 and Rs. 10,000, respectively. ‘A’ works as a manager and is entitled to draw a salary of 30% out of total profit. If at the end of the year, total amount received by ‘A’ is Rs. 4,000 more than that by ‘B’, then find the total profit earned from the business.

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

Ratio of profit shares of ‘A’ and ‘B’ = 12000 : 10000

= 6 : 5

Let the total profit made by the company be Rs. ‘11x’

A’s salary = 11x × 0.3 = Rs. ‘3.3x’

Profit left for distribution = 11x − 3.3x = Rs. ‘7.7x’

Profit share of ‘A’ = 7.7x × (6/11) = Rs. ‘4.2x’

Profit share of ‘B’ = 7.7x × (5/11) = Rs. ‘3.5x’

ATQ

4.2x + 3.3x − 3.5x = 4000

Or, 4x = 4000

So, x = 1000

∴ total profit earned by the business = 11 × 1000 = Rs. 11,000

25. ‘A’ and ‘B’ started a business by investing Rs. 3,200 and Rs. 4,000, respectively. It was decided that 50% of the profit will be divided equally, and rest of the profit will be divided in the ratio of their investment. At the end of the year, if ‘A’ gets Rs. 300 less than ‘B’, then find the total annual profit from the business.

Correct Answer: (b) Rs. 5,400
Solution:

Ratio of profits received by ‘A’ and ‘B’

= 3200 : 4000 = 4 : 5

Let, total annual profit earned from the business be Rs. ‘36x’

Half of total annual profit = (36x/2) = Rs. ‘18x’

So, profit share of ‘A’ = (18x/2) + (4/9) × 18x = Rs. ‘17x’

So, profit of ‘B’ = (18x/2) + (5/9) × 18x = Rs. ‘19x’

ATQ

(19x − 17x) = 300

2x = 300

So, x = 150

Therefore, total annual profit received = 150 × 36 = Rs. 5,400

26. ‘A’ and ‘B’ started a business by investing Rs. 800 and Rs. 900 for ‘y’ months and (y + 5) months respectively such that at the end of the business, out of the total profit of Rs. 7,400, the profit share of ‘B’ was Rs. 1000 more than that of ‘A’. Find the value of ‘y’.

Correct Answer: (b) 30
Solution:

Let the profit share of ‘A’ = Rs. K

Then, profit share of ‘B’ = Rs. (K + 1000)

So, K + K + 1000 = 2K + 1000 = 7400

So, K = (7400 − 1000) ÷ 2 = 3200
So, profit share of ‘A’ = Rs. 3200
And, profit share of ‘B’ = 7400 − 3200 = Rs. 4200

And so, ratio of profit shares of ‘A’ and ‘B’ is
3200:4200 = 16:21, respectively.

So, (800 × y):(900 (y + 5)) = 16:21

Or, 800y:(900y + 4500) = 16:21

Or, 16800y = 14400y + 72000

So, y = 72000 ÷ 2400 = 30

27. ‘A’, ‘B’ and ‘C’ started a business by investing Rs. 4,000, Rs. 4,500 and Rs. 6,000 where ‘C’ invested for 2 months more than ‘B’ and ‘A’ invested for 2 months less than ‘B’ such that the profit share of ‘C’ was 110% more than that of ‘A’. Find the number of months for which ‘B’ invested.

Correct Answer: (c) 12 months
Solution:

Let the number of months for which ‘A’ invested = ‘y’

Then, number of months for which ‘C’ invested = y + 2 + 2 = (y + 4) months

So, ratio of profit shares of ‘A’ and ‘C’ respectively
= (4000 × y):(6000 × (y + 4)) = 100:210

(4000y):(6000y + 24000) = 10:21

400y × 21 = 6000y + 24000

2400y = 24000

So, y = 10

And so, number of months for which ‘B’ invested
= y + 2 = 12 months.

28. ‘A’ and ‘B’ started a business by investing Rs. 4,000 and Rs. 2,500, respectively. Nine months later, ‘A’ decreased his investment by 25%. After 3 more months, ‘B’ increased his investment by 20%. If at the end of two years, the business earned a profit of Rs. 49,000, then find the profit share of ‘A’.

Correct Answer: (e) None of these
Solution:

Ratio of profit shares of ‘A’ and ‘B’ at the end of two years:

= {(4000 × 9) + (4000 × 0.75 × 15)} : {(2500 × 12) + (2500 × 1.2 × 12)}

= (36000 + 45000) : (30000 + 36000)

= 81000 : 66000 = 27 : 22

So, profit share of ‘A’ = 49000 × (27/49) = Rs. 27,000

29. ‘A’ and ‘B’ entered into a partnership with the investment of Rs. ‘x’ and Rs. (x + 1000), respectively. After 7 months, ‘A’ added Rs. 2,000 to his initial investment. If the ratio of annual profit shares of ‘A’ and ‘B’ is 29 : 30, respectively. Find the sum of the initial investment of ‘A’ & ‘B’.

Correct Answer: (c) Rs. 9,000
Solution:

Ratio of profit shares of ‘A’ and ‘B’
= {(x × 7) + (x + 2000) × 5} : {(x + 1000) × 12}

= (12x + 10000) : (12x + 12000)

Given,
(12x + 10000)/(12x + 12000) = (29/30)

360x + 300000 = 348x + 348000

12x = 48000

x = 4000

Initial investment of ‘A’ = x = Rs. 4,000

Initial investment of ‘B’ = (x + 1000)
= (4000 + 1000) = Rs. 5,000

Sum of the initial investments of ‘A’ and ‘B’
= 5000 + 4000 = Rs. 9,000

30. ‘A’ and ‘B’ started a business by investing Rs. 2250 and Rs. 4000 where ‘B’ invested for 5 months less than ‘A’. At the end of the business, out of the total profit of Rs. 4200, the profit share of ‘B’ was Rs. 2400. Find the number of months for which ‘A’ invested in the business.

Correct Answer: (b) 20
Solution:

Ratio of profit shares of ‘A’ and ‘B’
= (4200 − 2400) : 2400
= 1800 : 2400 = 3 : 4

Let the number of months for which ‘A’ invested = ‘y’

So, ratio of profit shares of ‘A’ and ‘B’
= (2250 × y) : (4000 × (y − 5))

= 2250y : (4000y − 20000) = 3 : 4

750y = 1000y − 5000

So, y = 5000 ÷ 250 = 20

Therefore, ‘A’ invested for 20 months