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Two shopkeepers, Bruce and Wayne, sold the same toy at different price 13 May 2020, 08:54
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56% (02:00) correct 44% (02:09) wrong based on 178 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.


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Two shopkeepers, Bruce and Wayne, sold the same toy at different price 14 May 2020, 00:23
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Bunuel
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.
Show more

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
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Two shopkeepers, Bruce and Wayne, sold the same toy at different price 14 May 2020, 00:31
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Bunuel
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.
Show more

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.
    • We need to find who made a greater profit.
      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 \((b – 3x ) > (w – 4x)\)
Hence, statement 1 is NOT sufficient and we can eliminate answer option A and D.

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, \((b – 3x) > (w – 4x)\)
    • Alternately,we can also think as Bruce spend less than Wayne as cost price of the toy and sold the toy at a higher price than Wayne.
      o So, profit of Bruce must be greater than Wayne.
Hence, statement 2 is sufficient.
Thus, the correct answer is Option B.
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Two shopkeepers, Bruce and Wayne, sold the same toy at different price 15 May 2020, 09:11
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chetan2u
Bunuel
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.

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
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hi chetan2u

Can you please elabarote more on highlighted part ? The ratio of selling toys 4b-3b=b is clear since purchased price was 3b and selling price is 4b hemce b is profit so its clear but how do you come up with "4a-3a or a less" and "profit of Bruce is more than that of Wayne by a+b. ' ?
maybe some simple figures would work for better understanding :grin:
thanks :)
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Two shopkeepers, Bruce and Wayne, sold the same toy at different price 15 May 2020, 11:49
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chetan2u
Bunuel
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.

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


hi chetan2u

Can you please elabarote more on highlighted part ? The ratio of selling toys 4b-3b=b is clear since purchased price was 3b and selling price is 4b hemce b is profit so its clear but how do you come up with "4a-3a or a less" and "profit of Bruce is more than that of Wayne by a+b. ' ?
maybe some simple figures would work for better understanding :grin:
thanks :)
Show more


Hi,
Say B and W purchased it in ratio 3:4, say 300:400..... B spent a or 100 less
They sold it in ratio 4:3, say 800:600... here B sold it for b or 200 more
So profit is a+b or 100+200=300 more.

So profit of B otherwise = 800-300=500, and that of W is 600-400=200.
Thus B is 500-200 or 300 more, which is nothing but a+b as shown above
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Two shopkeepers, Bruce and Wayne, sold the same toy at different price 21 Jun 2020, 03:56
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let
profit of B (Pb)
profit of W (Pw)

from statement 1 we get
\(\frac{Pb}{3x}*100>\frac{Pw}{4x}*100\)

\(Pb>\frac{3}{4}Pw\) ---condition

if Pb =1 and Pw =1
then the condition satisfies and profits are equal

now take Pb=2 and Pw=1
again the condition satisfied but now the profit of Pb is higher

two answers hence insufficient.

from statement 2 we get
4y-3x and 3y-4x
try putting some values you'll always get that 4y-3x is greater than 3y-4x

another approach
let 4y-3x>3y-x
y>-x
y+x>0 this is always true as since x and y are positive
hence sufficient
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Two shopkeepers, Bruce and Wayne, sold the same toy at different price 08 Jan 2026, 00:35
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It's late in the night. Bruce Wayne, after a long-day's stint of selling toys - an amiable profession the billionaire has taken to, to cope with the troubles of crimefighting all night - is accounting for the day's profits. He notices something strange: Half of the receipts say 'Bruce', the remaining half say 'Wayne'. That's when it hits him, the Joker's latest abomination - the "Personality Splitter", a diabolical device - has arrested his mind!

(He still needs to account for the profits though, but he notices, Bruce and Wayne - now split into two - proceeded to do business differently.)

Bruce, it turns out, bought the toy for $3, while Wayne, for $4. (This assuming values would account for the 3:4 ratio).

As Statement I states, Bruce's profit was higher than Wayne's. But it was clear even in the dead of the night to Bruce Wayne that this wasn't nearly enough information - the receipts highlighted, Bruce sold the $3 toy at a 10% profit (we plug in a value), amounting to a total sale of $9.90, and a profit of 90c. Wayne, on the other hand, sold four of his $4 toy at a 5% profit (plugging in a value - as the profit percentage of Bruce is higher as per the statement) - to a total sale of $16.80, or a profit of 80c. Any other value will lead to variable answers, so Statement I is not enough.

Not to be flummoxed any further, Bruce Wayne proceeded to the second statement - "The Ratio of prices at which Bruce and Wayne sold the toy was 4:3 respectively".

With a little help from Alfred, the billionaire had this figured out:

Now, even if Bruce had purchased his toy at 3c and Wayne at 4c, and sold it at, respectively, $40 and $30, we know for a fact that the $0.03 -> $40 will be a higher profit percentage than $0.04 -> $30. As the ratio for the cost prices shows one product more costly, and the ratio for the selling prices shows that same product as selling at a lower price, no matter the values, Bruce will always be more profitable than Wayne. Hence, B alone is sufficient.

The billionaire, after completing a hard day's work, decided to rest for the night. And as he did so, he muttered to himself, "I'm the mathematician GMAT deserves, not the one it needs right now".
Bunuel
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.


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