BANK & INSURANCE (PARTNERSHIP) PART 2

Total Questions: 45

1. Abhi, Bhanu and Chetan started a business. Abhi invested four times as much as Bhanu's investment and the investment of Chetan was x% less than that of Bhanu. At the end of one year, total profit of Rs. 7000 was earned, in which share of Abhi was Rs. 5000. What was the difference between the share of Bhanu and Chetan?

Correct Answer: (d) Rs.500
Solution:

Abhi investment = 4 × Bhanu’s investment

Chetan’s investment = Bhanu’s investment − x%

Total profit earned = Rs. 7000

Abhi’s share in total profit = Rs. 5000

Formula used
Calculation

Let the investment of Bhanu = Rs. 100a

Then the Investment of Abhi = 4 × 100a = Rs. 400a

And the investment of Chetan = (100 − x) % of 100a

⇒ Rs. (100a − ax)

The ratio profit of their investment = 400a : 100a : (100a − ax)

⇒ 400 : 100 : (100 − x)

Let us assume that the total profit

⇒ 400b : 100b : (100b − bx) = 7000

So Share of Abhi = 5000 / 7000 = 5 / 7

= 400 / (600 − x)

⇒ 600 − x = 560

⇒ x = 40

The ratio profit of their investment = 400 : 100 : (100 − 40)

⇒ 400 : 100 : 60

⇒ 20 : 5 : 3

Difference between share of Bhanu and Chetan

= 2 × 7000 / 28

= 500

Difference between share of Bhanu and Chetan is Rs. 500

2. A, B, and C entered into a partnership business. A invested Rs. x, B invested 20% more than A and C invested 25% more than B for the first 6 months. After 6 months A left the business and B withdrew half of his investment and left the business after 4 months whereas C increased his investment by 33(1/3)%. If at the end of year the difference between the profit share of C and (A + B) together is Rs. 1890, then find profit share of B.

Correct Answer: (a) Rs. 3360
Solution:

Ratio of Investment of A, B and C

= x : 6x/5 : 3x/2

= 10x : 12x : 15x

According to question,

Profit share of A : B : C

= (10x × 6) : (12x × 6 + 6x × 4) : (15x × 6 + 20x × 6)

⇒ 10x : 16x : 35x

⇒ C − (A + B) = Rs. 1890

⇒ 35x − (10x + 16x) = Rs. 1890

⇒ 9x = Rs. 1890

⇒ x = 210

Profit share of B = 16x

= 16 × 210

= Rs. 3360

∴ Profit of B is Rs. 3,360

3. A and B enter into a business and decided to distribute 60% of profit as per (investment × ratio) and rest in the ratio of 5 : 6. If the amount invested by A is 25% more than B and B withdraw 3/4th of his total investment after 9 months. Find the profit distribution ratio of A and B according to the given condition at the end of a year.

Correct Answer: (d) 6 : 5
Solution:

Let the total investment of B = 100

Investment of A = 100 × 125% = 125

Ratio of 60% profit

⇒ 125 × 12 : (100 × 9 + 100 × ¼ × 3)

⇒ 125 × 12 : 975

⇒ 20 : 13

Let the total profit is 330

Profit for A for only 60% of profit

= 330 × 60/100 × (20/33)

⇒ 120

Profit of B for only 60% of profit

= 330 × 60/100 × (13/33)

⇒ 78

Total profit of A

= 120 + (330 × 40/100) × 5/11

⇒ 120 + 60 = 180

Total profit of B

= 78 + (330 × 40/100) × 6/11

⇒ 78 + 72 = 150

Required ratio

= 180 : 150

= 6 : 5

∴ Profit ratio of A and B is 6 : 5

4. Rohan and Sohan started business with Rs. 2000 and Rs. 3000 respectively. After six-months, Rohan withdrew x% of his investment and Rajni replaced Sohan with x% of Sohan's Capital. After 1 year Rajni's share of profit is Rs. 1200 out of the total profit of Rs. 7400. Find the value of x?

Correct Answer: (e) 40
Solution:

For the first 6 months,

Investment of Rohan = Rs. 2000

Investment of Sohan = Rs. 3000

Investment of Rajni = Rs. 0

For the next 6 months,

Investment of Rohan

= Rs. (2000 − 2000 × x/100)

= Rs. (2000 − 20x)

Investment of Sohan = Rs. 0

Investment of Rajni

= Rs. 3000 × x/100

= Rs. 30x

∴ Effective ratio of their investments

= [2000 × 6 + (2000 − 20x) × 6] : 3000 × 6 : 30x × 6

⇒ 24000 − 120x : 18000 : 180x

⇒ 400 − 2x : 300 : 3x

According to problem,

3x / (x + 700) = 1200 / 7400

x = 40

5. Vansh and Aman started a business with Rs. 20000 and Rs. 24000 respectively as their capital investment. Shubham joined them after M months and invested Rs. 36 000 and M months before the end of year Aman left the business. If at the end of the year the share profit of Vansh, Aman and Shubham is in the ratio of 4 : 2 : 3, what is the value of M.

Correct Answer: (d) 7 months
Solution:

Ratio of their capital investment

⇒ 20000 : 24000 : 36000

⇒ 5 : 6 : 9

According to question

Ratio of time of investment

= 12 : 12 − M : 12 − M

Total ratio

= 5 × 12 : 6 × (12 − M) : 9 × (12 − M)

⇒ 60 : 72 − 6M : 108 − 9M

Ratio of profit of Vansh and Aman

⇒ 60 / (72 − 6M) = 4/2 (Cross Multiplication)

60 = 2 × (72 − 6M)

⇒ M = 7 Months

∴ The value of M is 7 Months.

6. Sachin and Kohli decided to invest in a business. They put in their capitals in the ratio of 5 : 3. However, in the next year sachin invested 40% more money and kohli withdrew 20% of his capital. If at the end of second year sachin got Rs 4000 as profit, then find the profit earned by kohli.

Correct Answer: (b) Rs. 1800
Solution:

Let the ratio of investment be x

And let the investments by sachin and kohli be

500x and 300x

∴ In 1st year, profit ratio will be,

Profit = 500x × 1 year : 300x × 1 year

Now, in the next year sachin invested 40% more

∴ Investment by sachin

= [(500x × 1) + (500x × 40/100) × 1]

⇒ 500x + 700x

⇒ 1200x

Also, kohli withdrew 20% of his capital.

∴ Investment for kohli

= [(300x × 1) + (300x × 80/100) × 1]

⇒ 300x + 240x

⇒ 540x

Ratio of profits = ratio of investments

⇒ Profit for sachin / profit for kohli

= 1200x / 540x

⇒ Profit for kohli

= (4000 × 540) / 1200

⇒ Profit for kohli

= 10 × 180 = 1800

∴ The profit earned by kohli is Rs 1800

7. A and B invested their capitals in the ratio of 3 : 1. After "x" months, A leaves and C joins with some capital. If they share the annual profit equally, then the capital invested by C was what % of the capital invested by A?

Correct Answer: (a) 50%
Solution:

Let the investment of A and B be 3y and y respectively

Time period of investment of A = x months

Time period of B = 12 months

Time period of C = (12 − x) months

Now, According to the question,

(3y × x) : (y × 12) = 1 : 1

3x : 12 = 1 : 1

⇒ x : 4 = 1

⇒ x = 4 months

Time period of C

= (12 − 4) months

⇒ 8 months

Now, if total profit is same, then investment will be inversely proportional to the time period

So, Ratio of investment of A and C = 8 : 4

Required percentage

= (4/8) × 100

⇒ 50%

∴ Required percentage is 50%

8. A and B started a business with Rs. 95000 and Rs. 57000 respectively. But B was a business partner and they decided to share their profit in the ratio of 4 : 3. If C joins with a condition that they will share profit and loss in the ratio of 2 : 1 : 3. Find the sacrifice ratio of A and B.

Correct Answer: (b) 10 : 11
Solution:

Sacrifice of A

= 4/7 − 2/6

= (24 − 14) / 42

= 10/42

Sacrifice of B

= 3/7 − 1/6

= (18 − 7) / 42

= 11/42

Sacrifice ratio

= Sacrifice of A : Sacrifice of B

⇒ 10/42 : 11/42

⇒ 10 : 11

∴ The sacrifice ratio will be 10 : 11.

9. Raja and Tulsi invested their capitals in a business in the ratio of 3 : 5 but for some reasons Raja withdraws half the amount after 4 months. If the total profit earned through this business is Rs 16800, then what will be the profit (in Rupees) received by Tulsi after the end of 12 months?

Correct Answer: (c) 12000
Solution:

Let the ratio of investments be x

And let the investment by raja and tulsi be 6x and 10x respectively.

⇒ Total investments for Raja = (6x × 4) + (3x × 8)
⇒ 24x + 24x
⇒ Total investments for Raja = 48x

Now, total investments for Tulsi = 10x × 12 = 120x

∴ Ratio of investments, Raja : Tulsi = 48x : 120x
⇒ 2 : 5

∴ Profit for Tulsi = 5/7 × 16800
⇒ 5 × 2400
⇒ Rs 12000

∴ The profit received by tulsi after 12 months is Rs 12000

10. Amar, Bittu and Chandan started a business with their investment in the ratio 3 : 6 : 4. After 8 months, Amar again invested the same amount as before. Bittu and Chandan withdraw half of their investment. What is the ratio of their profit at the end of the year?

Correct Answer: (c) 12 : 15 : 10
Solution:

Let investment of Amar, Bittu and Chandan be 3x, 6x and 4x respectively.

After 8 months Amar's amount = 3x + 3x
⇒ 6x

After 8 months Bittu's amount = 6x − (6x/2)
⇒ 3x

After 8 months Chandan's amount = 4x − (4x/2)
⇒ 2x

Now, Ratio of profit Amar, Bittu and Chandan

⇒ [(3x × 8) + (6x × 4)] : [(6x × 8) + (3x × 4)] : [(4x × 8) + (2x × 4)]

⇒ (24x + 24x) : (48x + 12x) : (32x + 8x)

⇒ 48x : 60x : 40x

⇒ 12 : 15 : 10

Ratio of profit A, B and C = 12 : 15 : 10

∴ The ratio of their profit at the end of the year will be 12 : 15 : 10.