If the difference between the compound interest and simple interest on a certain sum of money for three years at 10% p.a. is ₹ 558, then the sum is:

Let the principal sum = P

Rate = 10%

Time = 3 years

Compound interest on the sum = P$$\left(1+\frac{10}{100}\right)^3-$$ P = P$$\left(\frac{110}{100}\right)^3-$$ P = P$$\frac{1331}{1000}-$$ P = $$\frac{331}{1000}$$P

Simple interest on the sum = $$\frac{P\times3\times10}{100}$$ = $$\frac{3}{10}$$P

According to the problem,

$$\frac{331}{1000}$$P $$-$$ $$\frac{3}{10}$$P = 558

$$\Rightarrow$$  $$\frac{331P-300P}{1000}$$ = 558

$$\Rightarrow$$  $$\frac{31P}{1000}$$ = 558

$$\Rightarrow$$   P = 18000

$$\therefore\ $$The principal sum = ₹ 18,000

Hence, the correct answer is Option D