A sells a bicycle to B at a profit of 20% and B sells it to C at a profit of 25%. If C pays ₹1,500, then what

Question

A sells a bicycle to B at a profit of 20% and B sells it to C at a profit of 25%. If C pays ₹1,500, then what did A pay for it?

Examoogle · Accepted Answer

The correct answer is Option B: ₹1,000. Work backward from C's price using successive percentage multipliers: $$A = 1500 	imes \frac{100}{125} 	imes \frac{100}{120}$$.

Step-by-Step Solution & Concepts:
Shortcut Trick: Work backward from C's price using successive percentage multipliers: $$A = 1500 	imes \frac{100}{125} 	imes \frac{100}{120}$$.

Formula Used: $$C = A 	imes \left(1 + \frac{P_1}{100}ight) 	imes \left(1 + \frac{P_2}{100}ight)$$

Given: A sells a bicycle to B at 20% profit, B sells to C at 25% profit, and C pays ₹1,500.

Steps: Define variables and relationships: Let A's cost price be $x$. A sells it to B at a 20% profit, so the selling price to B (which is B's cost price) is $1.20x$.. Calculate B's selling price to C: B sells the bicycle to C at a 25% profit on B's cost price. Thus, C's purchase price is $1.25$ times B's cost price.. Equate and solve for A's cost price: Given that C pays ₹1,500, we equate $1.50x$ to $1500$ and solve for $x$.

Answer: B is correct because working backward from C's price of ₹1,500 gives A's cost price as $\frac{1500 	imes 100 	imes 100}{125 	imes 120} = 	ext{₹}1,000$.

Exam Tip: This successive percentage change formula is identical to compound interest and successive discounts used in commercial arithmetic.

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