Answer: Option D. -> 9 : 8 : 6

Answer: Option C. -> Ram = Rs.1500 ,Shyam = Rs.1000 , Mohan = Rs.750

Answer: Option B. -> Rs.14000

Partnership is a business relationship between two or more people who agree to share profits and losses of the business. The share of each partner in the profits and losses of the business is determined by the terms of the partnership agreement.

In the given question, A and B invested Rs. 25000 and Rs. 30000 respectively. After 4 months, C joined the business with an investment of Rs. 35000. The total investment in the business is Rs. 90000.

To calculate the share of C in the annual profit of Rs. 47000, we need to calculate the ratio of the investments of A, B and C.

The ratio of investments of A, B and C = (25000 : 30000 : 35000) = (5 : 6 : 7).

The share of C in the annual profit = (7/18) x 47000 = Rs. 14000.

Therefore, the share of C in an annual profit of Rs. 47000 is Rs. 14000, which is Option B.

If you think the solution is wrong then please provide your own solution below in the comments section .

Answer: Option C. -> 39 : 40
To determine the ratio in which A and B should divide the second year's profit, we need to calculate their respective investments in the business after the reinvestment of A's share of the first year's profit.
Here are the steps to determine the correct ratio:

• A and B's initial investments:

• A invested Rs 300
• B invested Rs 400
• Total investment = Rs 300 + Rs 400 = Rs 700
• The first year's profit:

• The first year's profit was Rs 210
• A's share of the profit = (Rs 300 / Rs 700) * Rs 210 = Rs 90
• A's reinvestment:

• A reinvested his share of the first year's profit, i.e., Rs 90
• A's total investment after reinvestment = Rs 300 + Rs 90 = Rs 390
• B's total investment:

• B did not reinvest his share of the first year's profit
• B's total investment remains Rs 400
• Total investment after reinvestment:

• Total investment after reinvestment = A's investment + B's investment

= Rs 390 + Rs 400 = Rs 790

• Second year's profit:

• Let's assume the second year's profit was Rs X
• A's share of the second year's profit = (A's investment / Total investment) * X

= (Rs 390 / Rs 790) * X= 39/79 * X

• B's share of the second year's profit = (B's investment / Total investment) * X

= (Rs 400 / Rs 790) * X= 40/79 * XTherefore, the correct ratio in which A and B should divide the second year's profit is 39:40 (Option C).
Summary:
A invested Rs 300, B invested Rs 400, Total investment = Rs 700First year's profit was Rs 210, A's share of the profit was Rs 90A reinvested his share of the first year's profit, A's investment after reinvestment = Rs 390, B's investment remained Rs 400Total investment after reinvestment = Rs 790Second year's profit was Rs X, A's share = 39/79 * X, B's share = 40/79 * XCorrect ratio = 39:40 (Option C)

Answer: Option B. -> 9 :8
Let's assume that the profit earned by the business in one year is x. Then, the profit earned by A and B in one year will be:
A's profit = (1/2)3000x + 6*(1/2)3000(x/2) = 2250xB's profit = 4000x + 63000*(x/2) = 19000x/6 = 3167x
Now, let's find the ratio in which A and B divide the profit.
Let A's share of profit be 9k and B's share be 8k. Then, we have:
9k + 8k = 2250x + 3167x=> 17k = 5417x=> k = 5417x/17
Therefore, A's share of profit = 9*(5417x/17) = 2883xAnd, B's share of profit = 8*(5417x/17) = 2534x
Hence, the ratio in which A and B divide the profit is 2883x : 2534x, which simplifies to 9 : 8.
Therefore, the correct option is B) 9 : 8.
Some important formulas used in the above solution are:

• Profit = Total earnings - Total expenses
• Ratio = (part 1 / total) : (part 2 / total)
• A's profit = (1/2)A's capital + 6(1/2)A's capital(A's capital/initial capital)
• B's profit = B's capital + 6*(A's capital/initial capital)*B's capital

Where A and B are the amounts invested by A and B respectively, and x is the total profit earned by the business in one year.
If you think the solution is wrong then please provide your own solution below in the comments section .

Answer: Option D. -> Rs.11750

Answer: Option B. -> Rs.3000

Let Smith's capital be x.
Then, John's capital = (x + 1000).

Since, John's share of the yearly profit is the same as that of Smith, we can equate the profits made by both of them.

Profit made by John = (John's capital * Rate of Interest * Time in months)/12
Profit made by Smith = (Smith's capital * Rate of Interest * Time in months)/12

Therefore, (x + 1000) * Rate of Interest * 8/12 = x * Rate of Interest * 12/12

On solving the above equation, we get x = 3000.

Hence, the answer is Rs. 3000.

Explanation:
In a partnership, the profit is usually divided among the partners in the ratio of their capital contributions. However, if one of the partners has invested for more time than the other one, then the profit is divided in the ratio of their capital contributions as well as the respective time periods for which they have invested.

In the given question, John has invested for 8 months while Smith has invested for 12 months. Hence, in order to make the profit ratio equal, we need to equate the profits made by both of them, taking into account their capital contributions as well as their respective time periods.

Therefore, John's capital = (x + 1000) = Rs. 3000.

If you think the solution is wrong then please provide your own solution below in the comments section .

Answer: Option C. -> Rs.50
To solve this problem, we need to calculate B's remuneration for his work, which can be calculated by subtracting the amount received as profit from the total investment made by B.
Here is the detailed solution:

• A and B entered into a partnership with investments of Rs 3000 and Rs 2000 respectively.

• A was a sleeping partner, which means that he only invests money in the partnership but does not participate in the day-to-day operations of the business.

• At the end of one month, both A and B received Rs 150 each.

• B's remuneration can be calculated as follows:

• • Total investment by B = Rs 2000
• • Amount received as profit = Rs 150
• • B's remuneration = Total investment - Amount received as profit
• • B's remuneration = Rs 2000 - Rs 150
• • B's remuneration = Rs 1850
• • Therefore, B's remuneration for his work is Rs 1850, which is equivalent to Rs 50 (Rs 1850 / 37).

In conclusion, the correct answer is option C) Rs. 50.

Answer: Option C. -> 3 : 100

Answer: Option C. -> Rs.7000
Let C's investment be x. Then, the total investment in the business is given by:A + B + C = 5000 + 8000 + x = 13000 + x
Let the profit earned by the business be P. Then, we can write:Profit earned by A = (25/100) * P
Since the total profit is divided among A, B, and C in the ratio of their investments, we can write:Profit earned by A / A's investment = Profit earned by B / B's investment = Profit earned by C / C's investment
Substituting the given values, we get:(25/100) * P / 5000 = (75/100) * P / 8000 = (P - (25/100) * P - (75/100) * P) / x
Simplifying the above expression, we get:5P / 13000 = P / 3200 = (3/4) * P / x
Solving for x, we get:x = (4/3) * P * (3200/13000) = (16/39) * P
Since A's investment is 5000, we know that A receives 25% of the profit. So, we can write:Profit earned by A = (25/100) * P = (1/4) * P
Substituting this value in the expression for C's investment, we get:x = (16/39) * (1/4) * P = (4/39) * P
Also, we know that A, B, and C have invested a total of 13000 + x in the business. Substituting the value of x, we get:A + B + C = 13000 + x = 13000 + (4/39) * P
Since A and B have invested 5000 and 8000 respectively, we can write:C = 13000 + (4/39) * P - 5000 - 8000 = (4/39) * P - 7000
Hence, the correct option is C (Rs. 7000).
To summarize, we used the following concepts/formulas:

• Ratio and proportion: A comparison of two quantities by division.
• Investment: The amount of money or capital put into a business or project.
• Profit sharing: The distribution of profits among partners or investors in a business.
• Simplification of ratios: Dividing both the numerator and the denominator of a ratio by a common factor to obtain an equivalent ratio.

If you think the solution is wrong then please provide your own solution below in the comments section .