₹6400 is lent at simple interest for a number of years that is numerically equal to the rate percent per annum. If the interest comes to ₹1600, the rate per annum is what percent?

With rate and time both $r$, the interest is $6400\times r\times r/100=64r^2$, so $64r^2=1600$ → $r^2=25$ → $r=5$. (Check: 5 years at 5% on ₹6400 gives ₹1600, whereas $r=4$ would give only ₹1024.) 25 stops at $r^2$ and never takes the square root; 12.5 comes from writing the interest as $6400\times 2r/100$, adding the rate and the time instead of multiplying them.