Explanation:

To find the single discount equivalent to two successive discounts of 10% and 5%, we need to calculate the combined effect of these discounts on an original price.

- First Discount (10%):

- The price after a 10% discount is 90% of the original price.

- Second Discount (5%):

- The price after an additional 5% discount is 95% of the already discounted price.

- Calculating the Combined Discount:

- Multiply the factors of the successive discounts: $0.9\times 0.95=0.855$.

- This gives 85.5% of the original price, meaning 14.5% was subtracted.

- Equivalent Single Discount:

- The equivalent single discount is therefore 14.5%.

- Option Analysis:

- Option 1: 85.5% (incorrect, represents the remaining price, not discount)

- Option 2: 90% (incorrect, way off)

- Option 3: 75.5% (incorrect, too high)

- Option 4: 14.5% (correct )