Successive discounts of $50\%$ and $40\%$ equal a single discount of:

Let the initial price be $100$.
After first discount of $50\%$, the price becomes:

$$100-50=50$$

After second discount of $40\%$ on the reduced price:

$$50-\left(\frac{40}{100}\times 50\right)=50-20=30$$

Total single discount equivalent:

$$100-30=70\%$$

Alternatively, using the formula for successive discounts $a\%$ and $b\%$:

$$\text{Single Discount}=\left(a+b-\frac{ab}{100}\right)\%$$

$$\text{Single Discount}=\left(50+40-\frac{50\times 40}{100}\right)\%=(90-20)\%=70\%$$