A, B and Center into partnership by making investments in the ratio 3: 5: 7. After a year C invests another Rs. 337600 while A withdraws Rs. 45600. The ratio of investments then changes to 14:29: 167. How much did A invest initially?

Options

A. Rs 233364.71
B. Rs 9600
C. Rs 141600
D. 233374.7

Answer

To solve the problem step by step, we will follow the given information and perform the necessary calculations.

### Step 1: Define the Initial Investments
Let the initial investments of A, B, and C be represented as:
- A's investment = 3X
- B's investment = 5X
- C's investment = 7X

### Step 2: Adjust for Withdrawals and Additional Investments
After one year:
- A withdraws Rs. 45600, so A's new investment becomes:
\[ \text{A's new investment} = 3X - 45600 \]
- C invests an additional Rs. 337600, so C's new investment becomes:
\[ \text{C's new investment} = 7X + 337600 \]

### Step 3: Set Up the New Ratio
According to the problem, the new ratio of investments is given as:
\[ \text{A's new investment} : \text{B's investment} : \text{C's new investment} = 14 : 29 : 167 \]
This can be expressed as:
\[ \frac{3X - 45600}{5X} = \frac{14}{29} \]
and
\[ \frac{7X + 337600}{5X} = \frac{167}{29} \]

### Step 4: Solve the First Ratio Equation
From the first equation:
\[ 29(3X - 45600) = 14(5X) \]
Expanding both sides:
\[ 87X - 1328400 = 70X \]
Rearranging gives:
\[ 87X - 70X = 1328400 \]
\[ 17X = 1328400 \]
\[ X = \frac{1328400}{17} = 78000 \]

### Step 5: Calculate A's Initial Investment
Now, substituting the value of X back to find A's initial investment:
\[ \text{A's initial investment} = 3X = 3 \times 78000 = 234000 \]

### Conclusion
Thus, A's initial investment is Rs. 234000.

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