We are given that Rs. 432 is divided amongst three workers, A, B, and C, in such a way that:

• 8 times A's share = 12 times B's share
• 12 times B's share = 6 times C's share

Let the shares of A, B, and C be denoted by $x$, $y$, and $z$, respectively.

Step 1: Translate the conditions into equations

From the given conditions:

1. $8x = 12y$ — This relates A's share to B's share.
2. $12y = 6z$ — This relates B's share to C's share.

We can simplify these equations.

• From $8x = 12y$, divide both sides by 4:
  $2x = 3y$
  So, $y = \frac{2x}{3}$ — Equation (1).

• From $12y = 6z$, divide both sides by 6:
  $2y = z$
  So, $z = 2y$ — Equation (2).

Step 2: Express everything in terms of $x$

Substitute $y = \frac{2x}{3}$ into $z = 2y$:

$z = 2 \times \frac{2x}{3} = \frac{4x}{3}$

Now, we know the shares of A, B, and C in terms of $x$:

• A's share: $x$
• B's share: $\frac{2x}{3}$
• C's share: $\frac{4x}{3}$

Step 3: Use the total sum to find $x$

The total sum is Rs. 432, so:

$x + \frac{2x}{3} + \frac{4x}{3} = 432$

Simplify the left side:

$x + \frac{6x}{3} = 432$ $x + 2x = 432$ $3x = 432$ $x = \frac{432}{3} = 144$

Step 4: Conclusion

A’s share is Rs. 144.

Thus, the correct answer is C) Rs. 144.

Would you like to go over any part of the solution or have further questions?

Here are some related questions you might find helpful:

1. How do you solve problems with ratios and proportions?
2. What is the method for handling combined share problems?
3. How do you deal with problems involving multiple variables?
4. What’s the difference between direct and inverse variation in share problems?
5. Can you solve a similar problem with more workers involved?

Tip: When dealing with share problems, always express each share in terms of a common variable before solving for the total.