Question

which is a better offer two successive discounts of 20% and 5% of single discount of 25% give reasons also

Answer 1

Hi there !
Here's the answer:

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¶¶¶ To compare the two successive discounts of 20% and 5% with a single discount of 25%, equivalent (or net) discount of successive discounts is to be calculated.

• Calculating Net discount of Successive discounts of 20% & 5% :

Let Marked Price be x
Now, Apply successive discounts of 20% & 5%

%Discount = 20%
Discount Price = Marked Price(1 - %Discount)
= x( 1 - 20%)
= x(1 - (20/100))
= x(80/100)
= 0.8x
This is price 1
To this again 5% Discount is availed.

%Discount =5%
Discount Price = Marked Price(1 - %Discount)
= 0.8x(1 - 5%)
= 0.8x(1 - (5/100))
= 0.8x(95/100)
= 0.8×0.95x
= 0.76x
This is final price.

Now find Equivalent discount of 20% & 5%
Let equivalent discount be 'd%'
0.76x = x - d% of x
=> d% of x = x( 1 - 0.76)
=> (d/100)×x = x(0.24)
=> d/100 = 0.24
=> d% = 24

Effective discount availed on two successive discounts of 20% and 5% is 24%

• Compare with single discount of 25%

Clearly, single discount of 25% is more than effective discounts of 20% and 5%(i. e., 24%)

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Hope it helps