$10+10\times 0$ equals $0$ or $10$ I thought $10+10\times 0$ equals $0$ because:
$$10+10 = 20$$
And
$$20\times 0 = 0$$
I know about BEDMAS and came up with conclusion it should be $$0$$ not $$10$$
But as per this, answer is $10$, are they right?

To elucidate what you said above in the original post, consider that $20\times0=0$, and consider also that $10+10=20$.  If we have two equations like that, with one number $n$ on one side of an equation by itself with $m$ on the other side of the equation, and $n$ also appearing in the middle of a formula elsewhere, we should then have the ability to replace $n$ by $m$ in the middle of the formula elsewhere.  The rule of replacement basically says this.  In other words, $20\times0=10+10\times0$, since $20=10+10$, and $20\times0=0$, we replace $20$ by $10+10$ in $20\times0=0$ and obtain $10+10\times0=0$, right?  But, BEDMAS says that $10+10\times0=10$.  Why the difference?
The catch here lies in that the $10+10\times0$ obtained in the first instance does NOT mean the same thing as $10+10\times0$, given by fiat, in the second instance.  Technically speaking, neither $20\times0=0$ and $10+10=20$ ends up as quite correct enough that you can use the rule of replacement as happened above.  More precisely, $20\times0=0$ abbreviates $(20\times0)=0$, and $10+10=20$ abbreviates $(10+10)=20$.  Keeping that in mind then we can see that using the rule of replacement here leads us to $((10+10)\times0)=0$ or more shortly $(10+10)\times0=0$.  BEDMAS says that $10+10\times0$ means $(10+(10\times0))$ or more shortly $10+(10\times0)$, which differs from $(10+10)\times0$.  So, the problem here arises, because the infix notation you've used makes it necessary to keep parentheses in formulas if you wish the rule of replacement as mechanically as you did.  
If you do express all formulas with complete parenthesis in infix notation, then BEDMAS becomes unnecessary.  If you wish to drop parentheses and use the rule of replacement mechanically as you did, then you'll need to write formulas in either Polish notation or Reverse Polish notation, or fully parenthesized infix notation, instead of partially parenthesized, "normal" infix notation.  If you wish to keep BEDMAS and like conventions around, and write in normal infix notation, then you have to refrain from applying the rule of replacement as mechanically as you did.  Conventional mathematicians and authors of our era generally appear to prefer the latter.  I don't claim to understand why they appear to prefer a notation that makes such a simple logical rule, in some cases at least, harder to use than needed.
