A sum of ₹12,000 was taken at simple interest at some rate. After four months, ₹6,000 more was added and the total principal was charged at double the earlier rate of interest. At the end of the year,if the total interest was ₹2,800, what was the initial rate of interest?

Let the rate of interest for the principal amount ₹12,000 = R%

Time for the principal amount ₹12,000 = 4 months = $$\frac{4}{12}$$ year = $$\frac{1}{3}$$ year

According to the problem,

Principal amount after 4 months = ₹12,000 + ₹6,000 = ₹18,000

Rate of interest after 4 months = 2R%

Time for the principal amount ₹18,000 = 8 months = $$\frac{8}{12}$$ year = $$\frac{2}{3}$$ year

At the end of the year, the total interest was ₹2,800

$$=$$>  $$\frac{12000\times\frac{1}{3}\times R}{100}+\frac{18000\times\frac{2}{3}\times2R}{100}=2800$$

$$=$$>  $$40\text{R}+240\text{R}=2800$$

$$=$$>  $$280\text{R}=2800$$

$$=$$>  $$\text{R}=10$$%

$$\therefore\ $$Initial rate of interest = R = 10%

Hence, the correct answer is Option A