What single discount is equivalent to successive discounts of 10% and 20%?

Question

James Allen · Accepted Answer

#18%# After an initial discount of #10%# you would pay #90%# of the original price. After a second #20%# discount you would pay #80%# of the initially discounted price or #80%# of #90%# of the original price. #80/100xx90/100xx" original price" = 72/100" original price" or #72%# or the original price. Paying #72%# of the original price implies a discount of #18%#

Sadie Alexander · Answer

undefined To find the equivalent single discount for successive discounts of 10% and 20%, you can use the formula:

$$ \text{Equivalent Discount} = 1 - \left(1 - \frac{d_1}{100}\right) \times \left(1 - \frac{d_2}{100}\right) $$

Substituting $ d_1 = 10 $ and $ d_2 = 20 $ into the formula:

$$ \text{Equivalent Discount} = 1 - \left(1 - \frac{10}{100}\right) \times \left(1 - \frac{20}{100}\right) $$

$$ \text{Equivalent Discount} = 1 - (1 - 0.1) \times (1 - 0.2) $$

$$ \text{Equivalent Discount} = 1 - (0.9) \times (0.8) $$

$$ \text{Equivalent Discount} = 1 - 0.72 $$

$$ \text{Equivalent Discount} = 0.28 $$

So, the equivalent single discount for successive discounts of 10% and 20% is 28%.