Explanation:

Let's find the ratio:

- Step 1: Let \(x\) be the amount lent to Shyam. Therefore, \(200,000 - x\) is lent to Sushil.

- Step 2: The interest from Shyam is \(0.06x\) and the interest from Sushil is \(0.10(200,000 - x)\).

- Step 3: According to the question, the total interest from both is Rs 18,000. Therefore:

$$0.06x + 0.10(200,000 - x) = 18,000$$

- Step 4: Solve the equation:

$$

0.06x + 20,000 - 0.10x = 18,000

$$

$$

-0.04x + 20,000 = 18,000

$$

$$

-0.04x = -2,000

$$

$$

x = 50,000

$$

- Step 5: Shyam pays \(0.06 \times 50,000 = 3,000\).

- Step 6: Sushil pays \(0.10 \times 150,000 = 15,000\).

- Step 7: Thus, the ratio of interest by Shyam to Sushil is \(3,000:15,000 = 1:5\).

- Conclusion: The correct answer is Option 2: 1:5.