Divide Rs 26000 among three persons in the ratio `(1)/(2): (1)/(3) : (1)/(4).`

Answer

To divide Rs 26000 among three persons in the ratio \( \frac{1}{2} : \frac{1}{3} : \frac{1}{4} \), we can follow these steps:

### Step 1: Express the Ratios
First, we need to express the given ratios in a more manageable form. The ratios are \( \frac{1}{2}, \frac{1}{3}, \) and \( \frac{1}{4} \).

### Step 2: Find a Common Denominator
To combine these fractions, we need to find a common denominator. The least common multiple (LCM) of the denominators (2, 3, and 4) is 12.

### Step 3: Convert the Ratios
Now, we can convert each ratio to have the common denominator of 12:
- \( \frac{1}{2} = \frac{6}{12} \)
- \( \frac{1}{3} = \frac{4}{12} \)
- \( \frac{1}{4} = \frac{3}{12} \)

So, the ratios can be rewritten as \( 6 : 4 : 3 \).

### Step 4: Calculate the Total Parts
Now, we add the parts of the ratio:
\[ 6 + 4 + 3 = 13 \text{ parts} \]

### Step 5: Calculate the Value of Each Part
Next, we need to find the value of each part by dividing the total amount (Rs 26000) by the total number of parts:
\[ \text{Value of each part} = \frac{26000}{13} = 2000 \]

### Step 6: Calculate Each Person's Share
Now we can calculate each person's share:
- **First Person's Share**: \( 6 \times 2000 = 12000 \)
- **Second Person's Share**: \( 4 \times 2000 = 8000 \)
- **Third Person's Share**: \( 3 \times 2000 = 6000 \)

### Final Shares
Thus, the shares of the three persons are:
- First Person: Rs 12000
- Second Person: Rs 8000
- Third Person: Rs 6000

### Summary
The final distribution of Rs 26000 among the three persons in the ratio \( \frac{1}{2} : \frac{1}{3} : \frac{1}{4} \) is:
- Rs 12000
- Rs 8000
- Rs 6000

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