Question

Is it true that x% of y = y% of x? Justify your answer. ​

Answer 1

Answer:

The Answer is True

There are two ways to prove that this answer is correct:

Method 1: By Assigning the values

Let's assign the value of x as 20 and y as 10

x% of y=y% of x

$\frac{20}{100} \times 10 = \frac{10}{100} \times 20 \\ \\ \frac{20}{10} = \frac{10}{10} \times 2 \\ 2 = 2$

Let's prove the answer with one more solution

$\sf \: x\% \: of \: y = y\% \: of \: x$

Let's assume x is 5 and y is 2

$5\%of \: 2 = 2\%5 \\ \frac{5}{100} \times 2 = \frac{2}{100} \times 5$

$\frac{1}{10} = \frac{1}{10}$

$\therefore \sf proved$

Method 2: By using L.H.S=R.H.S

L.H.S= x% of y

=(x×y)/100

=y/100×x

=y% of x =R.H.S

Therefore, L.H.S=R.H.S

⏩Proved⏪

Answer 2

Question:-

Is it true that x% of y = y% of x?

Required answer:-

True

Explanation:-

Now, we have to find if x% of y = y% of x

$\sf \footnotesize{LHS = x\% \: of \: y}$

$\sf \footnotesize{ = \frac{x}{100} \times y}$

$\sf \footnotesize{ = \frac{xy}{100} = x \times \frac{y}{100} = y\% \: of \: x}$

$\sf \footnotesize{ = RHS}$

LHS = RHS

Hence, the given statement is true.