In how many years will the simple interest on a sum of money be equal to the principal at the rate of $$16\frac{2}{3}$$ % per annum ?

Solution(By Examveda Team)

$$\eqalign{ & {\text{16}}\frac{2}{3} = \frac{{1 \to {\text{ Interest}}}}{{6 \to {\text{ Principal }}}} \cr & {\text{Let principal = 6}} \cr & {\text{Interest = 6}} \cr & {\text{Time = t years}} \cr & {\text{By using formula }} \cr & {\text{6}} = \frac{{6 \times 50 \times {\text{t}}}}{{3 \times 100}} \cr & \Rightarrow {\text{t}} = 6\,{\text{years}} \cr} $$

Alternate
Note : In such type of questions to save your valuable time think like the given way.
$$\eqalign{ & {\text{Rate}}\% \cr & {\text{ = 16}}\frac{2}{3}\% = \frac{{1 \to {\text{ Interest}}}}{{6 \to {\text{ Principal }}}} \cr & {\text{Represent for 1 years}} \cr & {\text{According to the question,}} \cr & {\text{Principal = Interest}} \cr & {\text{6 = 1}} \times {\text{6}} \cr & {\text{Hence,}} \cr & {\text{Time = 1}} \times {\text{6}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,{\text{ = 6 years}} \cr} $$
Note : If interest will be six times then time will also be six times.