The price of an article increases by 10% every year. If the difference between the prices at the end of the 3rd year and the 4th year was Rs. 423.5, what was the price of the article at the end of second year?

Correct option is C

Given:

Annual increase in price = 10%

Difference between prices at end of 4th and 3rd year = Rs. 423.5

Formula Used:
If a value increases by r% annually, then after n years:

Final Value = $$P \times \left(1 + \frac{r}{100}\right)^n$$​​

Solution:

Let the price at the end of 2nd year be P

Price at end of 3rd year = P × (1.1)

Price at end of 4th year = P×(1.1)²

Now,

​$$P \times (1.1)^2 - P \times 1.1 = 423.5$$​​

​$$P \times 1.1 (1.1 - 1) = 423.5$$​​

0.11P = 423.5

P = $$\frac{423.5}{0.11}$$​= 3850

Thus, Price at the end of second year = ₹3850