Divide ₹ 7200 among A, B and C in the ratio `(1)/(3) : (1)/(6) : (1)/(4)`

Answer

To solve the problem of dividing ₹7200 among A, B, and C in the ratio \( \frac{1}{3} : \frac{1}{6} : \frac{1}{4} \), we will follow these steps:

### Step 1: Find a common denominator for the ratios
The given ratios are \( \frac{1}{3}, \frac{1}{6}, \frac{1}{4} \). The least common multiple (LCM) of the denominators (3, 6, and 4) is 12.

### Step 2: Convert the ratios to have the same denominator
We will convert each fraction to have a denominator of 12:
- For \( \frac{1}{3} \):
\[ \frac{1}{3} = \frac{4}{12} \]
- For \( \frac{1}{6} \):
\[ \frac{1}{6} = \frac{2}{12} \]
- For \( \frac{1}{4} \):
\[ \frac{1}{4} = \frac{3}{12} \]

Thus, the ratios become \( 4 : 2 : 3 \).

### Step 3: Calculate the total parts in the ratio
Now, we add the parts of the ratio:
\[ 4 + 2 + 3 = 9 \text{ parts} \]

### Step 4: Determine the value of one part
To find the value of one part, we divide the total amount (₹7200) by the total number of parts (9):
\[ \text{Value of one part} = \frac{7200}{9} = 800 \]

### Step 5: Calculate the amounts for A, B, and C
Now, we can find the amounts for A, B, and C:
- Amount for A:
\[ A = 4 \text{ parts} = 4 \times 800 = 3200 \]
- Amount for B:
\[ B = 2 \text{ parts} = 2 \times 800 = 1600 \]
- Amount for C:
\[ C = 3 \text{ parts} = 3 \times 800 = 2400 \]

### Final Distribution
Thus, the amounts distributed are:
- A: ₹3200
- B: ₹1600
- C: ₹2400