GATE2016 CE-2: GA-4

Question

$(x\% \text{ of }y)$ + $(y\% \text{ of }x)$ is equivalent to ______ .

• A. $2\%$ of $xy$
• B. $2\%$ of $(xy/100)$
• C. $xy\%$ of $100$
• D. $100\%$ of $xy$

Answer 1

$X \%$ of $Y =\dfrac{X}{100}\times  Y= X\times \dfrac{Y}{100}\quad \to(1)$
and
$Y\%$ of $X =\dfrac{Y}{100}\times  X= Y\times \dfrac{X}{100}\quad \to(2)$

From equations $(1)$ and $(2$) it is clear that $X\%$ of $Y +$ as $Y\%$ of $X$

$=2\times \dfrac{XY}{100}$ which is equivalent to $2\%$ of $XY$

Hence, Answer is option  A

Comments

• $x\%\: \text{of}\: y = y\%\: \text{of}\: x$
• $x\%\: \text{of}\: y\%\:\text{of}\:A = 2x\%\: \text{of}\: y\%\:\text{of}\:\dfrac{A}{2} = 2x\%\: \text{of}\: 2y\%\:\text{of}\:\dfrac{A}{4}$ 

Answer 2

(X/100)(Y)+(Y/100)(X)=XY/50

So option  B 2% of XY is the answer

Answer 3

$x\% \text{ of } y$

=$\dfrac{x}{100} \times y$

=$\dfrac{xy}{100}$

$y\% \text{ of } x$

=$\dfrac{y}{100} \times x$

=$\dfrac{xy}{100}$

∴ $x\% \text{ of } y$ + $y\% \text{ of } x$

= $\dfrac{xy}{100}+\dfrac{xy}{100}$

= $\dfrac{2xy}{100}$

=$2\% \text{ of }xy$