A starts a business by investing Rs. 20,000. After 1 year B joins the business by investing Rs. 25,000. At the end of the third year, the profit earns by A is Rs. 1,84,656. Then find profit earns by B.
(a)Rs. 1,40,840
(b)Rs. 1,53,880
(c)Rs. 1,64,580
(d)Rs. 1,25,640

Options

A. Rs. 1,40,840
B. Rs. 1,53,880
C. Rs. 1,64,580
D. Rs. 1,25,640

Answer

To solve the problem step by step, we will calculate the profit earned by B based on the investment and time each partner contributed to the business.

### Step 1: Determine the time each partner invested
- A invests Rs. 20,000 for 3 years.
- B invests Rs. 25,000 for 2 years (since B joins after 1 year).

### Step 2: Calculate the capital contribution in terms of 'capital years'
- A's contribution in capital years = Investment × Time = 20,000 × 3 = 60,000
- B's contribution in capital years = Investment × Time = 25,000 × 2 = 50,000

### Step 3: Find the ratio of their contributions
- The ratio of A's to B's contributions = A's capital years : B's capital years = 60,000 : 50,000
- Simplifying this ratio gives us 6 : 5.

### Step 4: Calculate the total profit earned
- We know that A's profit is Rs. 1,84,656, which corresponds to the 6 parts of the profit.
- Therefore, let’s denote the total profit as 11 parts (6 parts for A and 5 parts for B).

### Step 5: Find the value of one part
- Total profit = A's profit + B's profit = 6 parts + 5 parts = 11 parts.
- If A's profit (6 parts) = Rs. 1,84,656, then:
\[ \text{Value of one part} = \frac{1,84,656}{6} = 30,776 \]

### Step 6: Calculate B's profit
- B's profit corresponds to 5 parts:
\[ \text{B's profit} = 5 \times \text{Value of one part} = 5 \times 30,776 = 1,53,880 \]

### Final Answer
- The profit earned by B is Rs. 1,53,880.