Question

(a% of a) + (b% of b) = 2% of ab then what percentage of a is b?

Answer 1

According to the question :

(a/100)a + (b/100)b = (2/100)ab
a^2 + b^2 = 2ab
(a-b)^2 = 0

a = b

Therefore b is 100 percent of a
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Answer 2

Given

(a% of a) + (b% of b) = 2% of ab

Find out the what percentage of a is b.

To proof

As given

(a% of a) + (b% of b) = 2% of ab

a% in written in the simple form

$=\frac{a}{100}$

b% is wrriten in the simple form

$= \frac{b}{100}$

2% is wrriten in the simple form

$= \frac{2}{100}$

than the equation is written in the form

$\frac{a\times a}{100} +  \frac{b\times b}{100} = \frac{2\times ab}{100}$

we get

a² + b² = 2ab

a² + b² - 2ab = 0

Formula  

(a+b)² = a² + b² + 2ab  

than the above equation becomes

( a + b )² = 0

thus

we get

a = b

Now find  out the what percentage of a is b.

FORMULA

$percentage = \frac{part\times 100}{whole}$

whole = b

part = a

put in the above formula

we get            

$= \frac{a\times 100}{b}$      

a = b ( prove above )

put in the above

$= \frac{a\times 100}{a}$

= 100 %

percentage of a is b be 100%

Hence proved