Question

By how much percent is four-fifth of 70 lesser than five sevenths of 112

• A. 24
• B. 30
• C. 38
• D. 25

Hint:

Always ensure you use the correct base (the value after "than") when calculating percentage comparisons. Here, the base is "five-sevenths of 112", which is 80.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
To find by what percentage one quantity is less than another, we first calculate the individual numerical values.
Then, we find their absolute difference and divide it by the reference value (the larger value), multiplying the result by 100.
Key Formula or Approach:
The percentage difference is calculated as:
\[ \text{Percentage Less} = \frac{\text{Larger Value} - \text{Smaller Value}}{\text{Larger Value}} \times 100 \]

Step 2: Detailed Explanation:
Let us calculate both values:
1. Calculate the first value (four-fifth of 70):
\[ \text{Value 1} = \frac{4}{5} \times 70 \]
\[ \text{Value 1} = 4 \times 14 = 56 \]
2. Calculate the second value (five sevenths of 112):
\[ \text{Value 2} = \frac{5}{7} \times 112 \]
\[ \text{Value 2} = 5 \times 16 = 80 \]
3. Determine by how much 56 is lesser than 80:
- Larger Value = 80
- Smaller Value = 56
\[ \text{Difference} = 80 - 56 = 24 \]
4. Calculate the percentage:
\[ \text{Percentage Less} = \frac{24}{80} \times 100 \]
\[ \text{Percentage Less} = \frac{3}{10} \times 100 = 30\% \]
This matches Option B.

Step 3: Final Answer:
The value is 30% lesser.