If A is 6 times more than B, then by what percentage is B is less than A ?

Options

A. `64.82`
B. `83.33`
C. `28.56`
D. `85.71`

Answer

To solve the problem, we need to understand the relationship between A and B clearly. The statement "A is 6 times more than B" can be interpreted mathematically.

### Step-by-Step Solution:

1. **Define the Variables:**
Let B = x (where x is any value for B).
According to the problem, A is 6 times more than B.

2. **Express A in terms of B:**
If A is 6 times more than B, then:
\[ A = B + 6B = 7B \]
This means A is 7 times B.

3. **Substitute the value of B:**
Since we defined B as x, we can write:
\[ A = 7x \]

4. **Calculate the difference between A and B:**
The difference between A and B is:
\[ A - B = 7x - x = 6x \]

5. **Calculate the percentage by which B is less than A:**
To find the percentage by which B is less than A, we use the formula:
\[ \text{Percentage} = \left( \frac{\text{Difference}}{\text{Value of A}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage} = \left( \frac{6x}{7x} \right) \times 100 \]

6. **Simplify the expression:**
The x in the numerator and denominator cancels out:
\[ \text{Percentage} = \left( \frac{6}{7} \right) \times 100 \]

7. **Calculate the final percentage:**
Now, calculate \( \frac{6}{7} \times 100 \):
\[ \text{Percentage} = 85.71\% \]

### Final Answer:
B is 85.71% less than A.

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