In an experiment the values of two spring constants were measured as $$k_{1}=(10\pm0.2)N/m\text{ and }k_{2}=(20\pm0.3)N/m$$. lf these springs are connected in parallel, then the percentage error in equivalent spring constant is :

Two springs with $$k_1 = (10 \pm 0.2)$$ N/m and $$k_2 = (20 \pm 0.3)$$ N/m are connected in parallel and we need to find the percentage error in the equivalent spring constant.

For springs in parallel, the equivalent spring constant is simply the sum, so $$ k_{eq} = k_1 + k_2 = 10 + 20 = 30 \text{ N/m}. $$

Since absolute errors add directly for addition, we have $$ \Delta k_{eq} = \Delta k_1 + \Delta k_2 = 0.2 + 0.3 = 0.5 \text{ N/m}. $$

Substituting these into the formula for percentage error gives $$ \% \text{ error} = \frac{\Delta k_{eq}}{k_{eq}} \times 100 = \frac{0.5}{30} \times 100 = 1.67\%. $$

Therefore, the correct answer is Option (1): 1.67%.