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