# A discount series of 10%, 20% and 40% is equivalent to a single discount of ???

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A discount series of 10%, 20% and 40% is equivalent to a single discount of ???
posted Dec 29, 2014

If 2 succesive discounts a% and b%
then net discount = a + b – (ab/100)

If 3 succesive discounts a%, b% and c%
then single discount
= a + b + c – (ab/100 + bc/100 + ca/100 – abc/10000)
In this case,
single discount
= 10 + 20 + 40 – (200/100 + 800/100 + 400/100 – 8000/10000)
= 70 – (14 – 0.8)
= 56.8 %

Say 100 is the price -
1. 1st 10 % discount means the sales price is 90
2. 2nd 20% discount on 90 means sales price is 72 (90-18)
3. 3rd 40% discount on 72 means sales price is 43.2 (72-28.8)

Total discount is 100-43.2 or 56.8%

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