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13 May 2020, 08:54
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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:
65%
(hard)
Question Stats:
53% (02:05) correct
47%
(02:15)
wrong
based on 114
sessions
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Two shopkeepers, Bruce and Wayne, sold the same toy at different prices. If the ratio of the prices at which Bruce and Wayne purchased the toy was 3:4 respectively, who made a greater profit on selling the toy?
(1) The profit percentage of Bruce was higher than that of Wayne.
(2) The ratio of the prices at which Bruce and Wayne sold the toy was 4:3 respectively.
Are You Up For the Challenge: 700 Level Questions
(1) The profit percentage of Bruce was higher than that of Wayne.
(2) The ratio of the prices at which Bruce and Wayne sold the toy was 4:3 respectively.
Are You Up For the Challenge: 700 Level Questions
14 May 2020, 00:23
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Bunuel
We do not know the exact amount but the ratio of cost to B and W = 3:4 =3a:4a
(1) The profit percentage of Bruce was higher than that of Wayne.
since we do not the exact values of cost or the profit %, we cannot say anything.
Say profit % on 3a is 50, then profit = 1.5a..
Now if profit % on 4a is 10, then profit is 0.4a <1.5a, but if the profit % is 40%, then profit is 1.6a>1.5a....
Insuff
(2) The ratio of the prices at which Bruce and Wayne sold the toy was 4:3 respectively.
So the selling prices are 4b and 3b.
Now Bruce purchased the toy at 4a-3a or a less, and sold it at higher price by 4b-3b=b. Thus, profit of Bruce is more than that of Wayne by a+b.
Suff
B
14 May 2020, 00:31
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Bunuel
Solution
Step 1: Analyse Question Stem
- • Let us assume that Bruce and Wayne sold the toys at prices b and w respectively.
• The cost price of the toy for Bruce and Wayne were in ratio 3:4
- o So, let us assume that the cost price for the Bruce and Wayne were 3x and 4x respectively.
- Where x is a positive number.
- o Or, which is greater among (b – 3x) and (w – 4x)
Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1: The profit percentage of Bruce was higher than that of Wayne.
- • \(\frac{(b – 3x)}{3x} > \frac{(w – 4x)}{4x }⟹(b – 3x) > \frac{3}{4}(w – 4x) ⟹ (b – 3x ) > 0.75(w – 4x)\)
• From this statement we cannot be sure if \((b – 3x ) > (w – 4x)\)
Statement 2: The ratio of the prices at which Bruce and Wayne sold the toy was 4:3 respectively.
- • It means, \(\frac{b}{w} = \frac{4}{3}\)
• Let us assume that b = 4y and w = 3y where y is a positive number.
• Since, y is positive, \(4y > 3y\)
- o Subtracting 3x from both side, we get,
o \(4y – 3x > 3y – 3x \)
o If \(4y - 3x > 3y - 3x\) then it is obvious that \(4y - 3x \) will be greater than \(3y - 4x\) ( since x is positive integer)
o Therefore, \((b – 3x) > (w – 4x)\)
- o So, profit of Bruce must be greater than Wayne.
Thus, the correct answer is Option B.
