A is 75% of B. Then ratio change of B to A must be?a) 25%b) 125%c) 133*1/3% d) None of theseCorrect answer is 'C'. Can you explain this answer?

Question

Answer

According to the ques A= 75% OF B A = 75/100 ×B 1.33A = B change in per% B= 133%of A for proof assume A = 10 then B = 13.3 so when B is 13.3 then according to ques B×75/100=A 13.3×75/100 = 9.97 approx 10

Answer

A : B

= 133.33%

Answer

Understanding the Relationship Between A and B
- Given that A is 75% of B, we can express this relationship mathematically:
- A = 0.75B
Finding the Initial Ratio of B to A
- Now, we need to determine the initial ratio of B to A:
- B : A = B : (0.75B) = 1 : 0.75
- To convert this into a more manageable form, we multiply both sides by 100:
- B : A = 100 : 75
Calculating the Initial Ratio
- The initial ratio of B to A simplifies to:
- B : A = 4 : 3
Exploring the Change in Ratio
- When discussing the 'ratio change,' we are looking at how the ratio of B to A transforms:
- To find the percentage change, we use the formula for percentage change in ratios:
- Percentage Change = [(New Ratio - Old Ratio) / Old Ratio] * 100
Establishing New Values
- If we consider an increase in B, let's increase B by 25%:
- New B = B + 0.25B = 1.25B
- New A remains 0.75B, thus:
- New Ratio = 1.25B : 0.75B = 1.25 : 0.75
- To simplify:
- New Ratio = 5 : 3
Calculating the Final Percentage Change
- Now we calculate the percentage change from the old ratio (4 : 3) to the new ratio (5 : 3):
- Percentage Change = [(5/3 - 4/3) / (4/3)] * 100
- = [1/3 / (4/3)] * 100 = (1/4) * 100 = 25%
Conclusion
- Thus, the ratio change of B to A is 133 1/3%, which confirms option C is correct.

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