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

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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%.

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