Question

Let me calculate & write the discount equivalent to succesive discounts of 20% , 10% & 5%
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Answer 1

The required single discount equivalent to the discount series of 20%, 10% and 5% is 31.6%

Now you must be curious as to how this came (coz

that's the reason you posted this question, right? :-P)

Here's the detailed explanation behind your answer:

Step 1: For ease, let's consider the initial amount to be Rs. 100

Step 2: Now the first discount is of 20%. So 20% of Rs. 100 = (20/100)*100 = Rs. 20

Step 3: Now left amount = 100 - 20 = Rs. 80

Step 4: Now the second discount is of 10%. So 10% of

Rs. 80 = (10/100)*80 = Rs. 8

Step 5: Now left amount = 80 - 8 = Rs. 72

Step 6: Now the third discount is of 5%. So 5% of Rs. 72

= (5/100)*72= Rs. 3.60

Step 7: Now left amount = 72-3.60 = Rs. 68.40

Step 8: So the overall discount offered = 100 - 68.40 = 31.60

Step 9: So the overall discount % offered = (31.60/100)*100 = 31.6%

Hence, The required single discount equivalent to the discount series of 20%, 10% and 5% is 31.6%

Answer 2

What will be a single discount equivalent to three successive discounts of 5%,10% and 20%?

If there are 3 successive discount of a, b, and c (percent).

Then the equivalent can be calculated within seconds using this expression

a+b+c−(ab+bc+ca)/100+abc/10000

Rest is just calculations, which will equal to 31.6