A's savings is `30%` less than B's savings, B's savings is `20%` less than C's savings. By what percentage is C's savings more than A's savings ?

Options

A. `63(2)/(7)%`
B. `52(1)/(3)%`
C. `64(3)/(5)%`
D. `78(4)/(7)%`

Explanation

To find out by what percentage C's savings is more than A's savings, we can follow these steps:

### Step 1: Assume C's Savings
Let's assume C's savings is `100` (in any currency).

### Step 2: Calculate B's Savings
Since B's savings is `20%` less than C's savings, we can calculate B's savings as follows:
- 20% of C's savings = 20% of 100 = 20
- Therefore, B's savings = C's savings - 20% of C's savings = 100 - 20 = `80`.

### Step 3: Calculate A's Savings
A's savings is `30%` less than B's savings. We can calculate A's savings as follows:
- 30% of B's savings = 30% of 80 = 24
- Therefore, A's savings = B's savings - 30% of B's savings = 80 - 24 = `56`.

### Step 4: Find the Difference Between C's and A's Savings
Now, we need to find out how much more C's savings is compared to A's savings:
- C's savings = 100
- A's savings = 56
- Difference = C's savings - A's savings = 100 - 56 = `44`.

### Step 5: Calculate the Percentage Increase
To find the percentage by which C's savings is more than A's savings, we use the formula:
\[ \text{Percentage Increase} = \left( \frac{\text{Difference}}{\text{A's Savings}} \right) \times 100 \]
Substituting the values:
\[ \text{Percentage Increase} = \left( \frac{44}{56} \right) \times 100 \]

### Step 6: Simplify the Calculation
Calculating the above expression:
- \(\frac{44}{56} = 0.7857\)
- Therefore, \(0.7857 \times 100 \approx 78.57\%\).

### Conclusion
C's savings is approximately `78.57%` more than A's savings.

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