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If A = x% of y and B = y% of x, then which of the following is true?
- a)A is smaller than B
- b)A is greater than B
- c)Relationship between A and B cannot be determined
- d)None of these
Correct answer is option 'D'. Can you explain this answer?
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If A = x% of y and B = y% of x, then which of the following is true?a)...
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If A = x% of y and B = y% of x, then which of the following is true?a)...
Explanation:
To determine the relationship between A and B, we need to understand the meaning of "x% of y" and "y% of x".
- "x% of y" means x% times y, which can be expressed as (x/100) * y.
- "y% of x" means y% times x, which can be expressed as (y/100) * x.
Let's substitute these expressions into the given equations:
A = (x/100) * y
B = (y/100) * x
Comparing A and B:
To compare A and B, we can simplify the expressions:
A = (x/100) * y = xy/100
B = (y/100) * x = xy/100
As we can see, A and B have the same value, xy/100. Therefore, A is equal to B.
Conclusion:
From the given equations and the comparison of A and B, we can conclude that A is equal to B. None of the given options (a, b, or c) is true.
Therefore, the correct answer is option 'D' - None of these.
To determine the relationship between A and B, we need to understand the meaning of "x% of y" and "y% of x".
- "x% of y" means x% times y, which can be expressed as (x/100) * y.
- "y% of x" means y% times x, which can be expressed as (y/100) * x.
Let's substitute these expressions into the given equations:
A = (x/100) * y
B = (y/100) * x
Comparing A and B:
To compare A and B, we can simplify the expressions:
A = (x/100) * y = xy/100
B = (y/100) * x = xy/100
As we can see, A and B have the same value, xy/100. Therefore, A is equal to B.
Conclusion:
From the given equations and the comparison of A and B, we can conclude that A is equal to B. None of the given options (a, b, or c) is true.
Therefore, the correct answer is option 'D' - None of these.
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