Asum of ₹5,000 is divided into two parts such that the simple interest on the first part for $$4\frac{1}{5}$$ years at $$6\frac{2}{3}\%$$ p.a is double the simple interest on the second part for $$2\frac{3}{4}$$ years at 4% p.a. What is the difference between the two parts?

Interest on 1st part = $$(r \times t)$$%
$$4\frac{1}{5} \times 6\frac{2}{3}$$% = $$\frac{221}{5} \times \frac{20}{3}$$%
= 28%
Interest on 2nd part,
$$2\frac{3}{4} \times 4$$% = $$\frac{11}{4} \times 4$$%
= 11%
Let the principle of 1st and 2nd part be p and q respectively.
ATQ,
28%p = 2$$\times$$ 11%q
14p = 11q
p : q = 11 : 14
(11 + 14 = 25) units = 5000
Difference between the two parts = 14 - 11 = 3 units
3 units = $$\frac{5000}{25} \times 3$$ = Rs.600
So, difference between the two parts is Rs.600.