The problem states that three successive discounts of 20%, 50%, and 10% are applied to an item. We need to find the single equivalent discount.

1. Problem Description

The problem states that three successive discounts of 20%, 50%, and 10% are applied to an item. We need to find the single equivalent discount.

2. Solution Steps

Let the original price of the item be $P$.

After the first discount of 20%, the price becomes $P_1 = P - 0.20P = 0.80P$.

After the second discount of 50%, the price becomes $P_2 = P_1 - 0.50P_1 = 0.50P_1 = 0.50(0.80P) = 0.40P$.

After the third discount of 10%, the price becomes $P_3 = P_2 - 0.10P_2 = 0.90P_2 = 0.90(0.40P) = 0.36P$.

The final price after all three discounts is $0.36P$. The total discount is $P - 0.36P = 0.64P$.

The equivalent single discount percentage is $\frac{0.64P}{P} \times 100\% = 0.64 \times 100\% = 64\%$.

3. Final Answer

The equivalent single discount is 64%.

Therefore, the answer is D) 64%.