Rs. 432 is divided amongst three workers A, B and C such that 8 times A's share is equal to 12 times B's share which is exqual to 6 times C's share. How much did A get?

Options

A. Rs. 192
B. Rs.133
C. Rs.144
D. Rs.128

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Set up the equations based on the given conditions.
We are given that:
- \( 8A = 12B = 6C \)

### Step 2: Express A, B, and C in terms of a common variable.
Let \( k \) be the common variable such that:
- \( 8A = k \)
- \( 12B = k \)
- \( 6C = k \)

From these equations, we can express A, B, and C as:
- \( A = \frac{k}{8} \)
- \( B = \frac{k}{12} \)
- \( C = \frac{k}{6} \)

### Step 3: Find a common denominator to combine the shares.
To combine these shares, we need a common denominator. The least common multiple (LCM) of 8, 12, and 6 is 24.

Now we can express A, B, and C in terms of the LCM:
- \( A = \frac{k}{8} = \frac{3k}{24} \)
- \( B = \frac{k}{12} = \frac{2k}{24} \)
- \( C = \frac{k}{6} = \frac{4k}{24} \)

### Step 4: Write the ratio of A, B, and C.
Now we can write the ratio of A, B, and C:
- \( A : B : C = 3k : 2k : 4k \)
This simplifies to:
- \( A : B : C = 3 : 2 : 4 \)

### Step 5: Calculate the total parts.
The total parts in the ratio are:
- \( 3 + 2 + 4 = 9 \)

### Step 6: Find the value of each part.
Since the total amount is Rs. 432, we can find the value of one part:
- Value of one part = \( \frac{432}{9} = 48 \)

### Step 7: Calculate A's share.
Now, we can find A's share:
- \( A's \, share = 3 \times 48 = 144 \)

### Final Answer:
Thus, A received Rs. 144.

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