In this question, we are given that when the numerator of a fraction is increased by 200% and the denominator is increased by 300%, the resultant fraction is 9/17.

To find the original fraction, we need to reverse the given changes.

Option 1: (frac{10}{17}) - Increasing the numerator by 200% would give us (frac{10}{17}) * 3 = (frac{30}{17}), which is not equal to the given resultant fraction of 9/17.

Option 2: (frac{11}{17}) - Similar to Option 1, increasing the numerator by 200% would give us (frac{11}{17}) * 3 = (frac{33}{17}), which is not equal to the given resultant fraction of 9/17.

Option 3: (frac{12}{17}) - Increasing the numerator by 200% gives us (frac{12}{17}) * 3 = (frac{36}{17}). Increasing the denominator by 300% gives us (frac{36}{17}) * 4 = (frac{144}{17}). This is equal to the given resultant fraction of 9/17. Therefore, option