If Rs. 810 divided among A, B and C are in ratio `1/4:2/5: 1 3/8` then the share of A will be

Options

A. Rs 100
B. Rs 160
C. Rs 550
D. Rs 200

Answer

To find the share of A when Rs. 810 is divided among A, B, and C in the ratio \( \frac{1}{4} : \frac{2}{5} : 1 \frac{3}{8} \), we can follow these steps:

### Step 1: Convert the mixed fraction to an improper fraction
The ratio given is \( \frac{1}{4} : \frac{2}{5} : 1 \frac{3}{8} \). First, we convert \( 1 \frac{3}{8} \) to an improper fraction:
\[ 1 \frac{3}{8} = \frac{8 \times 1 + 3}{8} = \frac{11}{8} \]
So, the ratios are:
\[ \frac{1}{4} : \frac{2}{5} : \frac{11}{8} \]

### Step 2: Find a common denominator
The denominators are 4, 5, and 8. The least common multiple (LCM) of these numbers is 40. We will convert each fraction to have a denominator of 40:
- For \( \frac{1}{4} \):
\[ \frac{1}{4} = \frac{1 \times 10}{4 \times 10} = \frac{10}{40} \]
- For \( \frac{2}{5} \):
\[ \frac{2}{5} = \frac{2 \times 8}{5 \times 8} = \frac{16}{40} \]
- For \( \frac{11}{8} \):
\[ \frac{11}{8} = \frac{11 \times 5}{8 \times 5} = \frac{55}{40} \]

### Step 3: Write the ratio in whole numbers
Now we can express the ratio of A, B, and C as:
\[ 10 : 16 : 55 \]

### Step 4: Calculate the total parts of the ratio
Now, we add the parts of the ratio:
\[ 10 + 16 + 55 = 81 \]

### Step 5: Calculate the share of A
To find A's share, we use the formula:
\[ \text{Share of A} = \left( \frac{\text{A's part}}{\text{Total parts}} \right) \times \text{Total amount} \]
Substituting the values we have:
\[ \text{Share of A} = \left( \frac{10}{81} \right) \times 810 \]

### Step 6: Simplify the calculation
Calculating this gives:
\[ \text{Share of A} = \frac{10 \times 810}{81} = 100 \]

Thus, the share of A is **Rs. 100**.

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