Divide Rs.6500 among A,B and C so that after spending 90% , 75% and 60% of their respective saving were in the ratio of 3: 5: 6

Answer

To solve the problem of dividing Rs. 6500 among A, B, and C based on their savings and spending ratios, we can follow these steps:

### Step 1: Determine the savings percentages
- A spends 90% of his savings, so he saves 10%.
- B spends 75% of his savings, so he saves 25%.
- C spends 60% of his savings, so he saves 40%.

### Step 2: Set up the savings in terms of a variable
Let the savings of A, B, and C be represented as:
- A's savings = 3x
- B's savings = 5x
- C's savings = 6x

### Step 3: Calculate the actual savings based on percentages
Now, we can express the actual savings in terms of x:
- A's savings (10% of A's total) = 0.10 * (3x) = 0.3x
- B's savings (25% of B's total) = 0.25 * (5x) = 1.25x
- C's savings (40% of C's total) = 0.40 * (6x) = 2.4x

### Step 4: Set up the equation for total savings
The total savings must equal Rs. 6500:
\[ 3x + 5x + 6x = 6500 \]
\[ 14x = 6500 \]

### Step 5: Solve for x
To find the value of x, divide both sides by 14:
\[ x = \frac{6500}{14} \]
\[ x = 464.29 \] (approximately)

### Step 6: Calculate individual savings
Now we can calculate the individual savings:
- A's savings = 3x = 3 * 464.29 = 1392.87 (approximately)
- B's savings = 5x = 5 * 464.29 = 2321.43 (approximately)
- C's savings = 6x = 6 * 464.29 = 2785.71 (approximately)

### Step 7: Verify the total savings
Now, let's verify that the total savings add up to Rs. 6500:
\[ 1392.87 + 2321.43 + 2785.71 = 6500 \]

### Step 8: Final distribution
Thus, the amounts that A, B, and C receive are approximately:
- A = Rs. 1392.87
- B = Rs. 2321.43
- C = Rs. 2785.71