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13 Apr 2026, 07:58
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
47% (03:37) correct
53%
(02:58)
wrong
based on 19
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A beach shop owner purchases beach umbrellas at a discount of \(a%\) off the list price. He then marks up the umbrellas and subsequently offers customers a discount of \(b%\) off the marked price. After the discount is applied, the owner earns a profit of \(c%\) of the final selling price.
The marked price is what percent of the original list price?
(A) \(100(1 - a)(1 - b)(1 - c)%\)%
(B) \(\frac{100(1 - a)}{(1 - b)(1 - c)}%\)%
(C) \(\frac{100(1 - a)}{1 - b - c}%\)%
(D) \(\frac{100}{(1 - b)(1 - c)}%\)%
(E) \(\frac{100(1 - a)(1 + b)}{1 - c}%\)%
The marked price is what percent of the original list price?
(A) \(100(1 - a)(1 - b)(1 - c)%\)%
(B) \(\frac{100(1 - a)}{(1 - b)(1 - c)}%\)%
(C) \(\frac{100(1 - a)}{1 - b - c}%\)%
(D) \(\frac{100}{(1 - b)(1 - c)}%\)%
(E) \(\frac{100(1 - a)(1 + b)}{1 - c}%\)%
17 Apr 2026, 13:45
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kevincan
\(a\%\) discount means \(= \frac{100-a}{100}\) or also can be written as \(1-a \) as in this question, variables already represent their percentage/decimal equivalent.
Owner purchased it at \(a\%\) discount of the list price hence \(( 1-a )l\) .... where \(l\) is the list price.
Owner sold it at \(b\%\) discount of the marked price hence \((1-b)m\) ... where m is the marked up price.
profit is \(c\% \) of sale price \(= c (1-b)m\)
(\(1-b)m - ( 1-a )l = c (1-b)m\)
\((1-b)m -c(1-b)m = (1-a)l\) ...re-arranging
\(m-mb-cm-cmb=(1-a)l\)
\(m(1-b) -mc(1-b)= (1-a)l\)
\((1-b)(m-mc) = (1-a)l\)
\(m(1-b)(1-c) = (1-a)l \)
\(m = \frac{ (1-a)l }{ (1-b)(1-c)}\)
\(\frac{m}{l}*100 = \frac{ (1-a) 100}{(1-b)(1-c)}\%\)
Ans B
Hope it helped.
