A father distributed Rs. 12250 among his four sons A, B, C and D such that
`("A's share")/("B's share")=("B's share")/("C's share") = ("C's share")/("D's share ") = 3/4`. Then find the share of C.

Answer

To solve the problem of distributing Rs. 12,250 among four sons A, B, C, and D based on the given ratios, we can follow these steps:

### Step 1: Define the Ratios
Given that:
\[ \frac{A}{B} = \frac{B}{C} = \frac{C}{D} = \frac{3}{4} \]
Let’s express the shares of A, B, C, and D in terms of a common variable \( k \).

### Step 2: Express Shares in Terms of k
From the ratio, we can write:
- \( A = 3k \)
- \( B = 4k \)
- \( C = \frac{4}{3}B = \frac{4}{3}(4k) = \frac{16k}{3} \)
- \( D = \frac{4}{3}C = \frac{4}{3}(\frac{16k}{3}) = \frac{64k}{9} \)

### Step 3: Find a Common Denominator
To combine these shares, we need to express them with a common denominator. The least common multiple of the denominators (1, 1, 3, 9) is 9. Thus, we can rewrite the shares:
- \( A = 3k = \frac{27k}{9} \)
- \( B = 4k = \frac{36k}{9} \)
- \( C = \frac{16k}{3} = \frac{48k}{9} \)
- \( D = \frac{64k}{9} \)

### Step 4: Sum of Shares
Now, we can add the shares:
\[ A + B + C + D = \frac{27k}{9} + \frac{36k}{9} + \frac{48k}{9} + \frac{64k}{9} = \frac{175k}{9} \]

### Step 5: Set Up the Equation
Since the total amount distributed is Rs. 12,250, we can set up the equation:
\[ \frac{175k}{9} = 12250 \]

### Step 6: Solve for k
To find \( k \), multiply both sides by 9:
\[ 175k = 12250 \times 9 \]
\[ 175k = 110250 \]
Now, divide both sides by 175:
\[ k = \frac{110250}{175} = 630 \]

### Step 7: Calculate C's Share
Now that we have \( k \), we can find C's share:
\[ C = \frac{48k}{9} = \frac{48 \times 630}{9} = 3360 \]

### Final Answer
Thus, the share of C is Rs. 3,360.

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