Find a single discount equivalent to successive discounts of 20%, 25% and 15%.

The correct option is 49%.

To find the single discount equivalent to successive discounts of 20%, 25%, and 15%, we can calculate the effective remaining price after each discount is applied sequentially to an initial marked price.

Let the initial marked price of the item be $P_0=100$.

Step 1: Apply the first discount of 20%
The price after the first discount becomes:
$P_1=100\times (1-\frac{20}{100})=100\times 0.80=80$

Step 2: Apply the second discount of 25%
The price after the second discount becomes:
$P_2=80\times (1-\frac{25}{100})=80\times 0.75=60$

Step 3: Apply the third discount of 15%
The final price after the third discount becomes:
$P_3=60\times (1-\frac{15}{100})=60\times 0.85=51$

Step 4: Calculate the total effective discount
The total discount amount on the initial price of 100 is:
$\text{Total Discount}=100-51=49$

Expressed as a percentage:
$\text{Single Equivalent Discount}=\frac{49}{100}\times 100\%=49\%$

Thus, the single equivalent discount is 49%.