Question

No one can solve this???????

Answer 1

It  is  a puzzle. For this, assume that  there are  two numbers  a and  b. then, the  answer of  the puzzle  can  be represented  like  this,

$a+b=\framebox{a-b}\framebox{a+b}$

On basis of  above  algorithm,

$6+4=\framebox{6\;-\;4}\framebox{6+10}=\framebox{2}\framebox{10}=210\\\;\\9+2=\framebox{9\;-\;2}\framebox{9+2}=\framebox{7}\framebox{11}=711\\\;\\8+5=\framebox{8\;-\;5}\framebox{8+5}=\framebox{3}\framebox{13}=313\\\;\\5+2=\framebox{5\;-\;2}\framebox{5+2}=\framebox{3}\framebox{7}=37\\\;\\7+6=\framebox{7\;-\;6}\framebox{7+6}=\framebox{1}\framebox{13}=113\\\;\\9+8=\framebox{9\;-\;8}\framebox{9+8}=\framebox{1}\framebox{17}=117\\\;\\10+6=\framebox{10\;-\;6}\framebox{10+6}=\framebox{4}\framebox{16}=416$$\\\;\\15+3=\framebox{15\;-\;3}\framebox{15+3}=\framebox{12}\framebox{18}=1218$

Now, let that  unknown numbers be  x  and  y. then we can say ,

$x+y=\framebox{x\;-\;y}\framebox{x+y}=123=\framebox{1}\framebox{23}\\\;\\\text{On Comparing,}\\\;\\x-y=1\;\;\;...........i)\\\;\\x+y=23\;\;\;..........ii)\\\;\\\text{Adding eq. i) and ii)}\\\;\\x-y+x+y=1+23\\\;\\2x=24\\\;\\x=12\\\;\\\text{Putting x=12 in equ i)}\\\;\\12-y=1\\\;\\y=12-1\\\;\\y=11$

Hence Required Numbers are 12 and  11.

$12+11=\framebox{12\;-\;11}\framebox{12+11}=\framebox{1}\framebox{23}=123$