A discount series of 10%, 20% and 40% is equal to a single discount of

Let the Marked price = M

Price after 10% discount = $$\frac{90}{100}\text{M}$$

Price after 20% discount = $$\frac{20}{100}\times\frac{90}{100}\text{M}$$

Price after 40% discount = $$\frac{40}{100}\times\frac{20}{100}\times\frac{90}{100}\text{M}$$ = $$\frac{432}{1000}\text{M}$$

Selling price = $$\frac{432}{1000}\text{M}$$

Overall discount% = $$\frac{M-\frac{432}{1000}M}{M}\times100=\frac{568}{1000}\times100=56.8\%$$

Hence, the correct answer is Option D