A certain sum amounts to ₹29,282 in 4 years at 10% p.a, when the interest is compounded yearly.What is the simple interest (in ₹) on the same sum for 5 years at the same rate?

Given, 

Amount = ₹29282

Rate = 10% 

Time = 4 years

As we know , 

$$A=P\left(1+\frac{r}{100}\right)^n$$

$$29282=P\left(1+\frac{10}{100}\right)^4$$

$$29282=P\left(\frac{11}{10}\times\ \frac{11}{10}\times\ \frac{11}{10}\times\ \frac{11}{10}\right)$$

By solving, We get

P = ₹20000

Now, 

R = 10%

Time = 5 year

Simple Interest =  $$\frac{P\times\ R\times\ T}{100}$$

= $$\frac{20000\times10\times\ 5}{100}=₹10000$$

Hence, Option A is correct