BANK & INSURANCE (PARTNERSHIP) PART 1

Total Questions: 75

21. X, Y and Z start a business. X and Z invest Rs.4500 and Rs.3600 respectively while Y invests 5/3rd of the amount invested by Z. At the end of twelve months, what will be the ratio of the shares of profit received by X and Y respectively?

Correct Answer: (a) 3:4
Solution:

Investment by Y = 5/3 × 3600 = 6000

Ratio of the shares of profit received by X and Y

= 4500 : 6000 = 3 : 4

22. Priya invests Rs.5000 in a scheme. After 6 months, Kunal also invested in the same scheme. After two years from the time of investment of Priya, the total profit received by them is Rs.10,045 out of which Kunal receives Rs.5145. What amount of money did Kunal invested initially?

Correct Answer: (b) Rs.7000
Solution:

Priya's investment = Rs.5000

She invests for 24 months

Total investment of Priya = 24 × 5000 = Rs.1,20,000

Kunal's investment = Rs. X

Kunal invests for (24 − 6) i.e. 18 months

Total investment of Kunal = 18 × X

Profit of Priya/profit of Kunal = [(10045 − 5145)/5145]

= 4900/5145 = 20/21

120000/18X = 20/21

X = 7000

Kunal invested Rs.7000 initially

23. In a partnership, P invests 16 2/3 % of the capital for one-sixth of the time, Q invests 1/3 of the capital for one-third of the time and R invests the rest of the capital for the whole time. What is the share of R if the profit is Rs.11500?

Correct Answer: (c) Rs.9000
Solution:

Let the total capital invested in the business be Rs. X
and the total time period be ‘Y’ months ⇒ P invested
16(2/3) % or (X/6) of capital for (Y/6) months
Q invested (X/3) of capital for (Y/3) months
R invests [X − (X/6) − (X/3)] = (X/2) for ‘Y’ months

Ratio of their profits = Ratio of the products of their
Investments and Time period P : Q : R = (X/6 × Y/6)
: (X/3 × Y/3) : (X/2 × Y)

⇒ P : Q : R = (1/36) : (1/9) : (1/2)

Multiplying each term in the ratio with LCM of (36, 9, 2) = 36

⇒ P : Q : R = 1 : 4 : 18

R's share = [18/(1 + 4 + 18)] × 11500
= (18/23) × 11500 = Rs. 9000

∴ R's share = Rs. 9000

24. A, B and C start a business by investing Rs 10,000 each. After 4 months of starting the business, A withdrew Rs 4000, B withdrew Rs 5000 and C invested Rs 6000 more. At the end of 9 months from the start of business, the profit earned by C is Rs 2250 more than the profit earned by A. The total profit from the business is

Correct Answer: (b) Rs 11475
Solution:Profit ratio of A, B and C = (10000 × 4 + 6000 × 5)
: (10000 × 4 + 5000 × 5) : (10000 × 4 + 16000 × 5)

= (10 × 4 + 6 × 5) : (10 × 4 + 5 × 5) : (10 × 4 + 16 × 5)

= (8 + 6) : (8 + 5) : (8 + 16)

= 14 : 13 : 24

Profit of C − Profit of A = 2250

24a − 14a = 2250

10a = 2250

a = 225

Total profit = 51a = 51 × 225 = Rs 11475

25. P starts a business, after 4 months Q also joined him with Rs 4200 and after 3 months of Q’s joining R also joined them with Rs 4200. If P gets Rs 4500 out of the total annual profit of Rs 13500 then find the value of initial investment of P?

Correct Answer: (d) Rs 2275
Solution:

Let the initial investment of P be ‘X’

Ratio of profit of P, Q and R = X × 12 : 4200 × 8 : 4200 × 5

P : Q : R = X : 2800 : 1750

Now, according to question

X / (X + 2800 + 1750) - (4500 / 13500)

X / (X + 4550) = 1 / 3

3X = X + 4550

2X = 4550

X = 2275

26. A, B, and C entered into a partnership. A invested 16 2/3% of the capital for 6 months, B invested 33 1/3% of the capital for 2 year and C invested rest of the capital for 2.5 years. At the end of 2.5 years, they earned Rs.9600 as the total profit. What is the share of profit of B?

Correct Answer: (b) Rs. 3200
Solution:

Ratio of share of profit of A, B and C
= (1/6 × 6) : (1/3 × 24) : (1/2 × 30)

= 1 : 8 : 15

The share of B = 9600 × 8/24 = Rs. 3200

27. Anu started a business by investing an amount of Rs.30000. Eight months later, Anuj joined her with an investment of Rs.45000. Find Anu's share in the profit of the business, if they earned a profit of Rs.9252 at the end of one year from the start of business.

Correct Answer: (b) Rs.6168
Solution:

Amount invested by Anu and Anuj
= Rs.30000 and Rs.45000 respectively.

Ratio of amount invested by Anu to Anuj = 2 : 3

Time period of Anu's and Anuj's investment
= 12 months and 4 months respectively.

Ratio of time periods of Anu to Anuj
= 12 : 4 = 3 : 1

Hence, Ratio of profits earned by Anu to Anuj
= (2 × 3) : (3 × 1) = 6 : 3 = 2 : 1

Total profit = Rs.9252

⇒ Anu's share = (2/3) × 9252 = Rs.6168

28. P and Q started a business by investing amount Rs.1200 and Rs.1800 more than the investment of R who joined them after 3 months. Q left after 9 months from the beginning of partnership. If at the end of one-year partnership, profit earned by P and Q are in the ratio 5 : 4 respectively, then what is the investment of R?

Correct Answer: (b) Rs.7800
Solution:

Let investment of R = a

Then, investment of P = 1200 + a

And, investment of Q = 1800 + a

Now, profit ratio, P : Q : R
= ((1200 + a) × 12) : ((1800 + a) × 9) : (a × 9)

Also, profit ratio, P : Q = 5 : 4

Then, 5 : 4 = ((1200 + a) × 12) : ((1800 + a) × 9)

a = Rs.7800

29. A started a business with investment of Rs.4000. Ratio of investment of A and B is 4:3 respectively. B invested for 12 months. Ratio of time period of investment for A and B is 1:2 respectively. Find the profit share of A out of total profit of Rs.5000.

Correct Answer: (b) Rs.2000
Solution:

Investment of B = 4000 × 3/4 = 3000

Time period of investment of A = 12/2 × 1 = 6 months.

A : B

4000 × 6 : 12 × 3000

2 : 3

Profit of A = 5000/5 × 2 = Rs.2000

30. Sahil and Aayush started a business together with initial capital in the ratio 5:4. After 3 years Aayush adds Rs.500 more to his capital and at the end of 5 years ratio of their profit is 25 : 21, then what is the initial capital of Sahil in the business?

Correct Answer: (c) Rs.5000
Solution:

Let initial capital of Sahil and Aayush is ‘5x’ and ‘4x’ respectively.

Profit weightage of Sahil = (5x × 5) = 25x

Profit weightage of Aayush

= (4x × 3) + [(4x + 500) × 2] = (20x + 1000)

Ratio of their profit = 25x : (20x + 1000) = 25 : 21

21x = 20x + 1000

x = 1000

Initial capital of Sahil in the business = 5x = Rs.5000