A, B & C started a business and invested in the ratio 7:6:5. Next Year, they increased their investment by 25%, 20% and 15%, respectively. In what ratio should profit earned only during 2ndyear be distributed?

Options

A. A) 155:144:175
B. B) 155:124:95
C. C) 135:147:152
D. D) 175:144:115

Answer

To solve the problem, we need to follow these steps:

### Step 1: Determine the Initial Investments
Let the initial investments of A, B, and C be represented as follows:
- A's investment = 7x
- B's investment = 6x
- C's investment = 5x

### Step 2: Calculate the Increased Investments for the Second Year
Next, we need to calculate the increased investments for the second year based on the given percentage increases:
- A increases his investment by 25%:
\[ \text{A's new investment} = 7x + 0.25 \times 7x = 7x \times 1.25 = 8.75x \]

- B increases his investment by 20%:
\[ \text{B's new investment} = 6x + 0.20 \times 6x = 6x \times 1.20 = 7.2x \]

- C increases his investment by 15%:
\[ \text{C's new investment} = 5x + 0.15 \times 5x = 5x \times 1.15 = 5.75x \]

### Step 3: Find the Ratio of Investments in the Second Year
Now, we need to find the ratio of their investments after the increase:
- A's investment = 8.75x
- B's investment = 7.2x
- C's investment = 5.75x

The ratio of A, B, and C's investments can be expressed as:
\[ \text{Ratio} = 8.75x : 7.2x : 5.75x \]
This simplifies to:
\[ 8.75 : 7.2 : 5.75 \]

### Step 4: Convert the Ratio to Whole Numbers
To make calculations easier, we can convert these decimal values to whole numbers by multiplying each term by a common factor. The least common multiple of the denominators (if we express them as fractions) can help us find a suitable multiplier.

Calculating:
- \(8.75 = \frac{875}{100} \)
- \(7.2 = \frac{72}{10} \)
- \(5.75 = \frac{575}{100} \)

To eliminate the decimals, we can multiply each term by 100:
\[ 875 : 720 : 575 \]

Now, we can simplify this ratio by dividing each term by their greatest common divisor (GCD). The GCD of 875, 720, and 575 is 5.

Dividing each term by 5:
\[ \frac{875}{5} : \frac{720}{5} : \frac{575}{5} = 175 : 144 : 115 \]

### Step 5: Final Ratio
Thus, the final ratio in which the profit earned during the second year should be distributed is:
\[ \text{Final Ratio} = 175 : 144 : 115 \]