Question : A sells a cycle to B at a profit of 20% and B sells it to C at a loss of 25%. If C bought the cycle for Rs. P, then the cost price of it for A was:
Option 1: $\operatorname{Rs. }\frac{1}{20}\mathrm{P}$
Option 2: $\operatorname{Rs. }\frac{9}{20}\mathrm{P}$
Option 3: $\operatorname{Rs. }\frac{9}{10}\mathrm{P}$
Option 4: $\operatorname{Rs. }\frac{10}{9}\mathrm{P}$
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Correct Answer: $\operatorname{Rs. }\frac{10}{9}\mathrm{P}$
Solution : Let the cost price of the cycle for A as $x$. Given that A sells the cycle to B at a profit of 20%. The selling price for A = $1.20x$ B sells it to C at a loss of 25%. The selling price for B $= 0.75\times1.20x = 0.90x$ Given that C bought the cycle for Rs. P. $⇒P = 0.90x$ $⇒x = \frac{1}{0.90}\mathrm{P}=\frac{10}{9}\mathrm{P}$ Hence, the correct answer is $\operatorname{Rs. }\frac{10}{9}\mathrm{P}$.
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