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What single discount is equivalent to two successive discounts of 10%

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What single discount is equivalent to two successive discounts of 10%  [#permalink]

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New post 27 Feb 2018, 22:47
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

83% (01:04) correct 17% (01:13) wrong based on 32 sessions

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What single discount is equivalent to two successive discounts of 10%  [#permalink]

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New post 27 Feb 2018, 23:42
Bunuel wrote:
What single discount is equivalent to two successive discounts of 10% and 15%?

(A) 25%

(B) 24%

(C) 24.5%

(D) 23.5%

(E) 22%



Whenever applying two successive discounts, the second discount must be a percentage
of the first discount. In this case, the first discount of 10% reduces the price of 100 to 90.

The second discount of 15% will be on the amount of 90, which is \(\frac{15}{100} * 90 = \frac{15*9}{10} = \frac{135}{10} = 13.5%\)

Therefore, the successive discounts add up to \(\frac{10+13.5}{100} = \frac{23.5}{100}\) = 23.5%(Option D) as a single discount
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Re: What single discount is equivalent to two successive discounts of 10%  [#permalink]

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New post 28 Feb 2018, 10:20

Solution



Let’s apply the successive discounts of 10% and 15% on amount x.

After discount of 10%, x becomes:

    • x – 10% of x = 0.9x

After discount of 15%, the final amount becomes:


    • 0.9x * (1-0.15)
    • x*0.9*0.85
    • 0.765 x

Therefore, final amount after successive discount is 0.765 x.

Now, we need to find equivalent discount to successive discounts of 10% and 15%. Let’s denote equivalent discount by ”d”.

Thus,

    • 0.765x= x- d % of x
    • 0.765x= x- d/100 * x
    • d/100 *x= 0.235 x
    • d= 23.5%

Thus, equivalent discount to 10% and 15% is 23.5%.

Answer: D
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What single discount is equivalent to two successive discounts of 10%  [#permalink]

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New post 28 Feb 2018, 10:24

Method 2:



Solution



We can simply use the formula \(A + B + \frac{(A * B)}{100}\) to find the successive discount.

    • Let's assume \(A = - 10\)% and \(B = -15\)%

    • Therefore, Final Discount \(= - 10 - 15 + \frac{(-10)(-15)}{100} = (-25 + 1.5)\) % \(= 23.5\) %

    • Thus, equivalent discount to \(10\)% and \(15\)% is \(23.5\)%.

Answer: D
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Re: What single discount is equivalent to two successive discounts of 10%  [#permalink]

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New post 01 Mar 2018, 17:32
1
Bunuel wrote:
What single discount is equivalent to two successive discounts of 10% and 15%?

(A) 25%

(B) 24%

(C) 24.5%

(D) 23.5%

(E) 22%


Ater an item is discounted by 10% and 15%, the price of the item is 0.9 x 0.85 = 0.765 of the original price. Thus, it is discounted by 1 - 0.765 = 0.235 = 23.5%.

Answer: D
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Re: What single discount is equivalent to two successive discounts of 10% &nbs [#permalink] 01 Mar 2018, 17:32
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