Question : A sells an article to B making a profit of $\frac{1}{5}$th of his outlay. B sells it to C, gaining 20%. If C sells it for Rs. 600 and incurs a loss of $\frac{1}{6}$th of his outlay, the cost price of the article for A is:
Option 1: Rs. 600
Option 2: Rs. 500
Option 3: Rs. 720
Option 4: Rs. 800
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Correct Answer: Rs. 500
Solution : Let the cost price of the article for A, B, and C as $x$, $y$, and $z$, respectively. Given that A sells an article to B making a profit of $\frac{1}{5}$th of his outlay. ⇒ $y = x + \frac{1}{5}x = \frac{6}{5}x$ B sells it to C, gaining 20%. ⇒ $z = y + 0.2y = 1.2y = 1.2×\frac{6}{5}x = \frac{36}{25}x$ C sells it for Rs. 600 and incurs a loss of $\frac{1}{6}$th of his outlay. ⇒ $600 = z - \frac{1}{6}z = \frac{5}{6}z = \frac{5}{6}×\frac{36}{25}x = \frac{6}{5}x$ Solving for $x$, $x = \frac{600×5}{6} = 500$ Hence, the correct answer is Rs. 500.
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