a% of a + b% of b = 2% of ab, then what percentage of a is b?a)50%b)75%c)100%d)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

A2 /100 + b2/100 =2ab/100 #a2 + b2 = 2ab. #a2 + b2 - 2ab = 0. #(a - b )2 = 0. #a- b = 0. # then a= b

Answer

Answer

Given problem: a% of a b% of b = 2% of ab, then what percentage of a is b?

To solve this problem, we need to understand the concept of percentages and fractions. Let's break down the given problem into parts and solve it step by step.

Step 1: Write the given equation in terms of fractions
a/100 * a/100 * b/100 * b/100 = 2/100 * a/100 * b

Step 2: Simplify the equation
a^2 * b^2 / 10000 = 2ab / 10000

a^2 * b^2 = 2ab

Dividing both sides by ab, we get:

ab = 2

Step 3: Find the percentage of b in terms of a
We know that ab = 2. We also know that a% of a is a/100 * a and b% of b is b/100 * b. So, we can write:

a/100 * a * b/100 * b = 2/100

a^2 * b^2 / 10000 = 2/100

a^2 * b^2 = 200

b^2 = 200 / a^2

b = sqrt(200 / a^2)

b = sqrt(2 * 100 / a^2)

b = sqrt(2) * 10 / a

b/a = sqrt(2) / 10

Therefore, b is (sqrt(2)/10) times a.

Step 4: Convert the fraction to a percentage
To convert the fraction to a percentage, we need to multiply it by 100. So,

b/a = (sqrt(2)/10) * 100 = (10 * sqrt(2))/10 = sqrt(2) * 10

Thus, b is approximately 14.14% of a.

Final Answer: Hence, the correct option is (c) 100%.

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