Two shopkeepers, Bruce and Wayne, sold the same toy at different price

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

• \(\frac{(b – 3x)}{3x} > \frac{(w – 4x)}{4x }⟹(b – 3x) > \frac{3}{4}(w – 4x) ⟹ (b – 3x ) > 0.75(w – 4x)\)
• From this statement we cannot be sure if \((b – 3x ) > (w – 4x)\)

• 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.