Question

If one number is $80\%$ of other and the sum of their square is $656$, then the numbers are ;

• A. $4,5$
• B. $8,10$
• C. $20,16$
• D. $14,12$

Answer 1

The correct option is C $20,16$

Let the two numbers be '$x$' and '$y$'.

It is given one number is $80\%$ of other,

i.e. $y=\frac{80}{100}\times x=0.8x$

Now, sum of the squares of both numbers is $656$

$x^2+y^2=656$

Substitute value of $y$

$x^2+(0.8x{)}^2=656$

$x^2+0.64x^2=656$

$1.64x^2=656$

$x^2=\frac{656}{1.64}=400$

$x\sqrt{400}$

$\Rightarrow x=20$

$y=0.8x$

$=0.8\times 20$

$y=16$

Required number are $20$ and $16$.