At a certain rate of simple interest, a certain sum doubles itself in 10 years. In how many years it will triple itself?

Since the sum doubles itself in 10 years, so sum = S.I. for 10 years.

Let the sum = x. 

Then, S.I. = x, and Time = 10 years.

we know that, S.I. = $\frac{\mathrm{P}\times \mathrm{R}\times \mathrm{T}}{100}$
∴ Rate = $\left(\frac{100 \times x}{x \times 10}\right)$% =10 %
Now, sum = x, S.I. = 2x, Rate = 10 %
∴ Time =$\left(\frac{100 \times 2x}{x \times 10}\right)$years = 20 years.

Hence, the correct answer is 20 yrs.