₹\(3500\) was lent partly at the rate of \(4\%\) and partly at the rate of \(6\%\) SI. The total interest received after \(3\) yr is ₹\(498\). What is the amount lent at the rate of \(4\%\) SI? \(3500\) টাকা আংশিকভাবে \(4\%\) এবং আংশিকভাবে \(6\%\) সরল সুদে ধার দেওয়া হয়। \(3\) বছর পরে মোট সুদ পাওয়া যায় \(498\) টাকা। \(4\%\) হারে কত টাকা ধার দেওয়া হয়েছিল?

Let amount lent at \(4\%\) = \(x\)

Then amount lent at \(6\%\) = \(3500 - x\)

Simple Interest formula:

\[ SI = \frac{PRT}{100} \]

Interest from \(x\) at \(4\%\) for \(3\) yr:

\[ \frac{x \times 4 \times 3}{100} = \frac{12x}{100} \]

Interest from \(3500 - x\) at \(6\%\) for \(3\) yr:

\[ \frac{(3500 - x) \times 6 \times 3}{100} = \frac{18(3500 - x)}{100} \]

Total interest = \(498\)

\[ \frac{12x}{100} + \frac{18(3500 - x)}{100} = 498 \]

Multiply both sides by \(100\):

\[ 12x + 18(3500 - x) = 49800 \]

\[ 12x + 63000 - 18x = 49800 \]

\[ -6x = -13200 \]

\[ x = 2200 \]

Amount lent at \(4\%\) = ₹\(2200\)

Correct Answer: D