Question

14. Find a single discount equivalent to two successive discounts of 20% and 10%.
costing 2
13. Which is a better offer: Two successive discounts of 20% and 5% or a​

Answer 1

Answer:

14. Two successive discounts of 15% and 20% are equal to single discount of 32%.

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

Step-by-step explanation:

14. Let the price of item on which the two successive discount of 15% and 20% applicable be 100

First discount of 15% on ₹100 = ₹15

Price after 15% Discount = ₹85

Successive discount of 20% will be applicable on price after 1st discount

20% of ₹85

20/100 × 85

= 85/5

= ₹17

Price of the item after second discount

= ₹85 - ₹17

= ₹68

Two successive discounts total = ₹15 + ₹ 17 = ₹32

As the price of the item before calculation was taken as ₹100 therefore the sum of successive discounts of 15% and 20% or single discount is equal to 32%

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 we could know that 25% is more effective discount.

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