On a sum of ₹64000 lent for 2 years, the compound interest exceeds the simple interest by ₹1000. The rate of interest per annum is what percent?

For 2 years the gap between compound and simple interest is P$(r/100{)}^2$, the interest earned on the first year's interest. So $64000\times (r/100{)}^2=1000$ → $(r/100{)}^2=0.015625$ → $r/100=0.125$ → $r=12.5$%. (Check: SI = ₹16000, while $64000\times 1.$$125^2$ = ₹81000 gives CI = ₹17000 — a difference of ₹1000.)