A single discount equivalent to three simple discounts of 10%, 12%, and 15% is:

The successive discounts are 10%,12% and 15%

Let the Initial value be 100.  

According to question, $$100\times\ \frac{\left(100-10\right)}{100}\times\ \frac{\left(100-12\right)}{100}\times\ \frac{\left(100-15\right)}{100}$$

i.e; $$100\times\ \frac{90}{100}\times\ \frac{88}{100}\times\ \frac{85}{100}$$

Discounted value = 67.32 % 

Equivalent discount = initial value - discounted value 

= 100 - 67.32 = 32.68 .

Hence option A is correct. 

Another method : 

Discount is also called successive decrease 

if x and y are two successive discounts then , 

$$x\ +\ y\ -\frac{\left(x\times\ y\right)}{100}$$

first we take first two discount 10% and 12%

$$\therefore\ 10\ +\ 12\ -\frac{10\times\ 12}{100}=\ 20.8\ \%$$

Now we take, 

20.8% and 15% ,

$$\therefore\ 20.8\ +\ 15\ -\frac{20.8\times\ 15}{100}=\ 32.68\ \%$$