The successive discounts of 30%. 25% and 15% is equivalent to a single discount of:

Let the marked price (M.P.) of the article be assumed as $$\text{Rs.}\,100$$. Choosing a convenient round figure keeps calculations simple without affecting the percentage result.

First discount: $$30\%$$ off.
Price left after first discount $$= 100 \times (1 - 0.30) = 100 \times 0.70 = \text{Rs.}\,70$$.

Second discount: $$25\%$$ off on the reduced price.
Price left after second discount $$= 70 \times (1 - 0.25) = 70 \times 0.75 = \text{Rs.}\,52.5$$.

Third discount: $$15\%$$ off on the latest reduced price.
Price left after third discount $$= 52.5 \times (1 - 0.15) = 52.5 \times 0.85 = \text{Rs.}\,44.625$$.

The final selling price (S.P.) is therefore $$\text{Rs.}\,44.625$$ when the original marked price was $$\text{Rs.}\,100$$.

Equivalent single discount $$(\%)$$ is found by comparing the reduction directly:
Total reduction $$= 100 - 44.625 = 55.375$$.
Hence, equivalent single discount $$= \dfrac{55.375}{100} \times 100\% = 55.375\%$$.

Therefore, the three successive discounts of $$30\%$$, $$25\%$$, and $$15\%$$ are together equal to one single discount of $$55.375\%$$.

Option B which is: 55.375%