A sum of Rs. 16800 is divided into two parts. One part is lent at a simple rate of interest of 6% per annum and the other part at 8% per annum. After 2 years the total sum received is Rs. 19.000. Find the sum lent at the rate of 6% and 8% respectively.

Correct option is A

​$$\textbf{Given:} \\\text{Total sum} = ₹16800 \\\text{Total amount received after 2 years} = ₹19000 \\\text{So, Total Interest} = 19000 - 16800 = ₹2200 \\\textbf{Let:} \\x = \text{Amount lent at 6\%} \\\Rightarrow (16800 - x) = \text{Amount lent at 8\%} \\\textbf{Simple Interest Formula:} \quad SI = \frac{P \times R \times T}{100} \\\text{Interest on } x \text{ at 6\% for 2 years:} \\SI_1 = \frac{x \times 6 \times 2}{100} = \frac{12x}{100} \\\text{Interest on } (16800 - x) \text{ at 8\% for 2 years:} \\SI_2 = \frac{(16800 - x) \times 8 \times 2}{100} = \frac{16(16800 - x)}{100} \\\textbf{Total Interest:} \\\frac{12x}{100} + \frac{16(16800 - x)}{100} = 2200 \\\text{Multiply the entire equation by 100:} \\12x + 16(16800 - x) = 220000 \\12x + 268800 - 16x = 220000 \\-4x + 268800 = 220000 \\-4x = 220000 - 268800 = -48800 \\x = \frac{48800}{4} = 12200 \\\textbf{Therefore:} \\\text{Amount lent at 6\%} = ₹12200 \\\text{Amount lent at 8\%} = 16800 - 12200 = ₹4600 \\$$

Correct answer is (a) 12200, 4600.