A sum of money put out at compound interest amounts in 2 years to Rs. 578.40 and in 3 years to Rs. 614.55. Find the rate of interest?

Clearly the difference between Rs. 578.40 and Rs.614.55 is the interest on Rs. 578.40 for 1 year.
∴ Interest on Rs. 578.40 for 1 year = Rs. 614.55 - Rs. 578.40 = Rs. 36.15
∴ Interest on Rs.100 for 1 year = Rs. (36.15 x 100)/578.40
= Rs. 3615/57840 x 100/1
= Rs. 6.25
= Rs. 6¹/₄
∴ The required rate is .6¹/₄ percent.