Question

Square of two more than a two digit number is multiplied and divided by 2 and 5 respectively. If twice of the result is equal to 500 then find the number? 

Answer 1

The answer is 23. Hope it is correct.

Answer 2

Answer: The two digit number is 23.

Step-by-step explanation:

Given that:

A two digit number, let it be x.

Two more than the two digit number be x+2.

Now its square is multiply and divided by 2 and 5,

that is;  $\frac{(2+x)^{2} *2}{5}$

twice of above value is equal to 500,

that is; $\frac{(x+2)^{2} *2}{5}*2=500$    (equation 1)

Finding the two digit number:

Solving the equation 1;

$(x^{2} +2^{2} +2*2*x)*\frac{4}{5} =500$

$(x^{2} +4+4x)*\frac{4}{5} =500$

Further solving, we get;

$(x+2)^{2} =\frac{2500}{4}$

$(x+2)^{2} =\frac{(50)^{2} }{(2)^{2} }$

$x+2=25$

$x=23$

Hence, the two digit number is 23.