Himanshu invested Rs 42000 in business . After 4 months , Kapil joins him with an investement of Rs P . If at the end of the year the profit is Rs 62000 and profit share of Himanshu is Rs 42000 . Find the value of P .

Options

A. A)Rs 25000
B. B)Rs 30000
C. C)Rs 28000
D. D)Rs 38000

Answer

To solve the problem step by step, we will analyze the investments made by Himanshu and Kapil, the time they invested, and the profit distribution.

### Step-by-Step Solution:

1. **Identify the Investments and Time:**
- Himanshu's investment = Rs 42,000
- Kapil's investment = Rs P (unknown)
- Time invested by Himanshu = 12 months (1 year)
- Time invested by Kapil = 8 months (since he joins after 4 months)

2. **Calculate the Investment Time Product:**
- For Himanshu:
\[ \text{Investment Time Product} = 42000 \times 12 = 504000 \]
- For Kapil:
\[ \text{Investment Time Product} = P \times 8 \]

3. **Set Up the Profit Sharing Ratio:**
- The total profit at the end of the year = Rs 62,000
- Himanshu's share of the profit = Rs 42,000
- Kapil's share of the profit = Total profit - Himanshu's profit = \(62000 - 42000 = 20000\)

4. **Establish the Ratio of Profits:**
- The profit ratio is based on the investment time products:
\[ \frac{Himanshu's \, Profit}{Kapil's \, Profit} = \frac{504000}{8P} \]
- We know that:
\[ \frac{42000}{20000} = \frac{21}{10} \]

5. **Set Up the Equation:**
\[ \frac{504000}{8P} = \frac{21}{10} \]

6. **Cross Multiply to Solve for P:**
\[ 504000 \times 10 = 21 \times 8P \]
\[ 5040000 = 168P \]

7. **Solve for P:**
\[ P = \frac{5040000}{168} = 30000 \]

Thus, the value of P is Rs 30,000.

### Final Answer:
The value of P is Rs 30,000.