Let's assume the principal amount be P.

Amount A after n years:

A = P + P * 0.1 * n

We desire to double the amount, so

A =2P.

And so: 2P=P+P*0.1n

We can make it even simpler thus:

P=P*0.1n

Dividing both sides by P:

1=0.1n

Solve for n:

n=1/0.1 =10

Hence, it will take 10 years for the amount to double at a 10% per annum simple interest.