The increase in the price of a certain item was 25%. Then the price was decreased by 20% and then again increased by 10%. What is the resultant increase in the price?

The correct option is 10%.

To find the resultant increase in the price of the item, we can trace the step-by-step price changes starting with an assumed initial price of the item.

Let the initial price of the item be $P$ (or we can assume a convenient value like 100 for simplicity).

Step 1: First increase of 25%
When the price is increased by 25%, the new price ($P_1$) becomes:
$$P_1=P+0.25P=1.25P$$

Step 2: Decrease of 20% on the new price
Next, this new price is decreased by 20%. The updated price ($P_2$) is calculated as:
$$P_2=P_1\times (1-0.20)$$
Substituting the value of $P_1$ from Step 1:
$$P_2=1.25P\times 0.80=1.00P$$
After this step, the price returns exactly to the initial price $P$.

Step 3: Third increase of 10%
Finally, the price is increased again by 10%. The final price ($P_3$) becomes:
$$P_3=P_2\times (1+0.10)$$
Substituting $P_2=1.00P$:
$$P_3=1.00P\times 1.10=1.10P$$

Step 4: Calculate the resultant percentage increase
The net increase is the difference between the final price and the initial price:
$$\text{Net Increase}=1.10P-P=0.10P$$
Expressing this as a percentage of the initial price:
$$\text{Resultant Percentage Increase}=\frac{0.10P}{P}\times 100\%=10\%$$

Thus, the overall resultant increase in the price of the item is 10%.