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27 Feb 2018, 23:47
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Difficulty:

35% (medium)

Question Stats:

62% (01:28) correct 38% (01:25) wrong based on 34 sessions

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The net price of a certain article is $306 after successive discounts of 15% and 10% off the marked price. What is the marked price? (A)$234.09

(B) $400 (C)$382.50

(D) $408 (E) None of these _________________ Intern Joined: 23 May 2015 Posts: 24 Re: The net price of a certain article is$306 after successive discounts  [#permalink]

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Updated on: 28 Feb 2018, 00:15
Net price given = $306 Discounts D1= 15% D2= 10% Marked price be M M*(1-D1)*(1-D2 )= 306 M = 306/(0.85*0.9) = 400 Answer should be B To win the Game , Be in the Game Please give Kudos for right Answers _________________ PLEASE PRESS KUDOS FOR CORRECT ANSWERS AND IF IT HELPS Originally posted by chandan1988 on 28 Feb 2018, 00:10. Last edited by chandan1988 on 28 Feb 2018, 00:15, edited 1 time in total. Senior SC Moderator Joined: 22 May 2016 Posts: 3557 The net price of a certain article is$306 after successive discounts  [#permalink]

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02 Mar 2018, 16:11
Bunuel wrote:
The net price of a certain article is $306 after successive discounts of 15% and 10% off the marked price. What is the marked price? (A)$234.09

(B) $400 (C)$382.50

(D) $408 (E) None of these With successive discounts on the same item, multiply the multipliers. P = Original price$306 = (% decrease)*(% decrease) * P

$$306=(.85)(.9)P$$
$$306 = .765P$$
$$P =\frac{306}{.765}=$$
$$P = 400$$

The arithmetic with decimals is lengthy.
Alternatives:
1) Try fractions, and reduce them.
$306 = (fraction)*P 15 percent discount = $$.85=\frac{85}{100}=\frac{17}{20}$$ 10 percent discount = $$.90=\frac{90}{100}=\frac{18}{20}$$ $$306 =(\frac{17}{20}*\frac{18}{20})P=(\frac{306}{400})P$$ $$306=\frac{306}{400} P$$ $$P=(\frac{400}{306})*(306)= 400$$ ANSWER B 2) Use a shortcut formula* and estimate. With two successive percent changes: A = first decrease B = second decrease We can find total decrease with this shortcut: $$A + B + \frac{(A*B)}{100}$$ $$-15 +(-10)+\frac{(-15)*(-10)}{100}$$ $$-25 +\frac{150}{100}= -25 + 1.5= -23.5$$ % 23.5% is a little less than 25% = $$\frac{1}{4}$$ $$1 -\frac{1}{4}^{-}=\frac{3}{4}^{+}$$ The discounted price will be a little higher than $$\frac{3}{4}$$ of the original. Answers:$306 $$\approx{\frac{3}{4}}$$ of Answers B and D.
Which one? B) $400, would be $$\frac{306}{400}=\frac{300}{400}+\frac{6}{400} >\frac{3}{4}$$ -- but not greater by much. Perfect. ANSWER B Check D. We do NOT want an exact match: $$\frac{3}{4}*408=306$$. That's exact. INCORRECT. *See VeritasPrepKarishma , Successive Percent Changes (scroll down). I cannot get the precise link to copy properly. _________________ SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here. Instructions for living a life. Pay attention. Be astonished. Tell about it. -- Mary Oliver The net price of a certain article is$306 after successive discounts   [#permalink] 02 Mar 2018, 16:11
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