A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2490 ?

Options

A. A) Rs. 820
B. B) Rs. 830
C. C) Rs. 840
D. D) Rs. 850

Answer

To solve the problem step by step, we need to determine how much share A gets from the total profit of Rs. 2490 based on their capital contributions.

### Step 1: Determine the total capital contribution
Let the total capital be \( x \).

- A contributes \( \frac{1}{3} \) of \( x \)
- B contributes \( \frac{1}{4} \) of \( x \)
- C contributes \( \frac{1}{5} \) of \( x \)
- D contributes the rest

### Step 2: Calculate the contributions of A, B, and C
We calculate the contributions of A, B, and C:

- A's contribution: \( \frac{x}{3} \)
- B's contribution: \( \frac{x}{4} \)
- C's contribution: \( \frac{x}{5} \)

### Step 3: Find D's contribution
To find D's contribution, we first need to calculate the total contribution of A, B, and C:

\[ \text{Total contribution of A, B, and C} = \frac{x}{3} + \frac{x}{4} + \frac{x}{5} \]

To add these fractions, we need a common denominator. The least common multiple (LCM) of 3, 4, and 5 is 60.

Converting each fraction:

- \( \frac{x}{3} = \frac{20x}{60} \)
- \( \frac{x}{4} = \frac{15x}{60} \)
- \( \frac{x}{5} = \frac{12x}{60} \)

Now, adding these:

\[ \frac{20x}{60} + \frac{15x}{60} + \frac{12x}{60} = \frac{47x}{60} \]

Thus, D's contribution is:

\[ D's \ contribution = x - \frac{47x}{60} = \frac{60x - 47x}{60} = \frac{13x}{60} \]

### Step 4: Determine the ratio of contributions
Now we have the contributions:

- A: \( \frac{x}{3} = \frac{20x}{60} \)
- B: \( \frac{x}{4} = \frac{15x}{60} \)
- C: \( \frac{x}{5} = \frac{12x}{60} \)
- D: \( \frac{13x}{60} \)

The ratio of their contributions is:

\[ A : B : C : D = 20 : 15 : 12 : 13 \]

### Step 5: Calculate the total parts in the ratio
Total parts = \( 20 + 15 + 12 + 13 = 60 \)

### Step 6: Calculate A's share of the profit
A's share of the profit can be calculated using the formula:

\[ \text{A's share} = \left( \frac{\text{A's part}}{\text{Total parts}} \right) \times \text{Total profit} \]

Substituting the values:

\[ \text{A's share} = \left( \frac{20}{60} \right) \times 2490 \]

Calculating this:

\[ \text{A's share} = \frac{1}{3} \times 2490 = 830 \]

### Final Answer
A's share in the profit is Rs. 830.

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