A sum of Rs. 50,250 is divided into two parts such that he simple interest on the first part for $$7\frac{1}{2}$$ years at $$8\frac{1}{3}\% $$  p.a. $$\frac{5}{2}$$ is times the simple interest on the second part for $$5\frac{1}{4}$$ years at 8% p.a. What is the difference (in Rs.) between the two parts?

Solution (By Examveda Team)

$$\eqalign{ & {\text{S}}{\text{.I}}{{\text{.}}_1} = \frac{5}{2} \times {\text{S}}{\text{.I}}{{\text{.}}_2} \cr & \frac{{x \times 25 \times 15}}{{100 \times 3 \times 2}} = \frac{5}{2} \times \frac{{y \times 8 \times 21}}{{100 \times 4}} \cr & 25 \times 5 \times x = 5 \times 2 \times 21 \times y \cr & x:y = 210:125 = 42:25 \cr & = 42 - 25 = 17{\text{ units}} \cr & 67{\text{ units}} = 50250 \cr & 1{\text{ unit}} = 750 \cr & 17{\text{ units}} = 750 \times 17 = 12750 \cr & {\text{Difference between both parts}} = 12750 \cr} $$