If Rs. 8400 is divided among A, B and C in the ratio $\frac{1}{5}:\frac{1}{6}:\frac{1}{10}$, what is the share of A ?

Question

Accepted Answer

To determine the share of A when Rs. 8400 is divided among A, B, and C in the ratio $\frac{1}{5}:\frac{1}{6}:\frac{1}{10}$, we need to follow these steps:

1. **Calculate the Common Denominator:**
   - The given ratios are $\frac{1}{5}$, $\frac{1}{6}$, and $\frac{1}{10}$.
   - The least common multiple (LCM) of the denominators 5, 6, and 10 is 30.

2. **Convert Ratios to a Common Base:**
   - Convert each ratio to have a denominator of 30:
     - $\frac{1}{5} = \frac{6}{30}$
     - $\frac{1}{6} = \frac{5}{30}$
     - $\frac{1}{10} = \frac{3}{30}$

3. **Determine the Total Parts:**
   - Add the parts of the ratios: $6 + 5 + 3 = 14$.

4. **Calculate the Share of A:**
   - A's share is $\frac{6}{14}$ of the total amount Rs. 8400.
   - Calculate A's share: $\frac{6}{14} \times 8400 = \frac{3600}{1} = 3600$.

Therefore, the share of A is Rs. 3600, which corresponds to Option 3.

**Explanation for Other Options:**

- **Option 1: Rs. 1800**
  - This option is incorrect because it does not reflect the correct calculation of A's share based on the given ratio. The calculation shows that A's share is Rs. 3600, not Rs. 1800.

- **Option 2: Rs. 3000**
  - This option is incorrect because it underestimates A's share. The correct calculation, as shown, results in Rs. 3600 for A's share.

- **Option 4: Rs. 4000**
  - This option is incorrect because it overestimates A's share. The correct calculation confirms that A's share is Rs. 3600.

In conclusion, the correct answer is Option 3: Rs. 3600, as it accurately reflects the share of A based on the given ratio and total amount.