330 was divided among A, B and C. If A

had received Rs. 10 less, B Rs. 15 less

and C Rs. 5 less, their shares would have

been in the proportion 1:2:3. What did C

get?

Let's solve the problem by defining the shares and using the information given.

### Step 1: Define the original shares
Let the original shares of A, B, and C be \( A \), \( B \), and \( C \) respectively.

### Step 2: Define the adjusted shares
According to the problem, if:
- A had received Rs. 10 less, A's share would have been \( A - 10 \).
- B had received Rs. 15 less, B's share would have been \( B - 15 \).
- C had received Rs. 5 less, C's share would have been \( C - 5 \).

With these adjustments, the shares would be in the proportion 1:2:3. Therefore, we have:
\[
A - 10 : B - 15 : C - 5 = 1 : 2 : 3
\]

### Step 3: Express the adjusted shares using a common multiple
Let the adjusted shares be \( x \), \( 2x \), and \( 3x \) respectively. This gives us the following equations:
\[
A - 10 = x \quad \text{(1)}
\]
\[
B - 15 = 2x \quad \text{(2)}
\]
\[
C - 5 = 3x \quad \text{(3)}
\]

### Step 4: Solve for \( A \), \( B \), and \( C \)
We can express \( A \), \( B \), and \( C \) in terms of \( x \):
\[
A = x + 10 \quad \text{(4)}
\]
\[
B = 2x + 15 \quad \text{(5)}
\]
\[
C = 3x + 5 \quad \text{(6)}
\]

### Step 5: Use the total sum of the shares
The total amount is Rs. 330, so:
\[
A + B + C = 330
\]

Substituting the expressions for \( A \), \( B \), and \( C \) from equations (4), (5), and (6) into this equation:
\[
(x + 10) + (2x + 15) + (3x + 5) = 330
\]

Simplify:
\[
x + 10 + 2x + 15 + 3x + 5 = 330
\]
\[
6x + 30 = 330
\]

### Step 6: Solve for \( x \)
\[
6x = 330 - 30
\]
\[
6x = 300
\]
\[
x = \frac{300}{6} = 50
\]

### Step 7: Find the original share of C
Using \( x = 50 \) in equation (6):
\[
C = 3x + 5 = 3(50) + 5 = 150 + 5 = 155
\]

So, C's original share is Rs. 155.

Would you like more details or have any questions?

Here are five related questions:
1. What would be B's original share given this distribution?
2. How would the shares change if the total amount was Rs. 660 instead of Rs. 330?
3. If the proportions were 2:3:4 instead of 1:2:3, what would C's share be?
4. What if A had received Rs. 20 less instead of Rs. 10 less?
5. How does changing the total amount affect each person's share?

**Tip:** When dealing with ratios, always try to express the unknowns in terms of a single variable, as it simplifies solving the problem.

Learn how to solve a proportional distribution problem involving shares of A, B, and C. Understand how adjusting their shares affects the distribution ratio. Suitable for high school students studying proportion and linear equations.

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