At what rate of simple interest per annum will a sum of money become three times itself in 16 years?

Becoming three times means the interest earned is twice the principal: $2P=(P\times r\times 16)/100$ → $r=200/16=12.5$% per annum. (Taking the interest as just one principal gives 100/16 = 6.25%, which is the rate at which the sum merely doubles.)