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A cycle was sold at a gain of 10%. Had it been sold for 260RS. more, the gain would have been 14%. Find the cost price of the cycle.​

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Answer 1

$\huge\boxed{\textsf{\textbf{\pink{Given\::-}}}}$

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• A cycle was sold at a gain of 10 %. Had it been sold for Rs. 260 more, the gain would have been 14 %.

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$\huge\boxed{\textsf{\textbf{\green{To\:Find\::-}}}}$

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• Cost price (C.P) of the cycle?

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$\huge\boxed{\textsf{\textbf{\blue{Solution\::-}}}}$

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• Let selling price (S.P) be Rs. x.

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$\qquad \footnotesize \bf{\dag}\:\underline{\sf{In\:1^{st}\:case}}$

$\\ :\implies\:\sf Gain = 10\:\%$

$\\ :\implies\:\sf Gain = x + 10\:\%\: \times\:x$

$\\ :\implies\:\sf Gain = x + \dfrac{10}{100}\: \times\:x$

$\\ :\implies\:\sf Gain = x + \dfrac{10\: \times\:x}{100}$

$\\ :\implies\:\sf Gain = x + \dfrac{10x}{100}$

$\\ :\implies\:\sf Gain = \dfrac{100x + 10x}{100}$

$\\ :\implies\:\sf Gain = \dfrac{110x}{100}$

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$\qquad \footnotesize \bf{\dag}\:\underline{\sf{In\:2^{nd}\:case}}$

$\\ :\implies\:\sf Gain = 14\:\%$

$\\ :\implies\:\sf Gain = x + 14\:\%\: \times\:x$

$\\ :\implies\:\sf Gain = x + \dfrac{14}{100}\: \times\:x$

$\\ :\implies\:\sf Gain = x + \dfrac{14\: \times\:x}{100}$

$\\ :\implies\:\sf Gain = x + \dfrac{14x}{100}$

$\\ :\implies\:\sf Gain = \dfrac{100x + 14x}{100}$

$\\ :\implies\:\sf Gain = \dfrac{114x}{100}$

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Now,

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$\underline{\sf{\bigstar\:According\:to\:the\:given\:Question\::-}}$

$\\ :\implies\:\sf \dfrac{114x}{100} = \dfrac{110x}{100} + 260$

$\\ :\implies\:\sf \dfrac{114x}{100} - \dfrac{110x}{100} = 260$

$\\ :\implies\:\sf \dfrac{114x - 110x}{100} = 260$

$\\ :\implies\:\sf \dfrac{4x}{100} = 260$

$\\ :\implies\:\sf 4x = 260\:\times\:100$

$\\ :\implies\:\sf 4x = 26000$

$\\ :\implies\:\sf x = {\cancel{\dfrac{26000}{4}}}$

$\\ :\implies\:\underline{\boxed{\textsf{\textbf{\purple{x = 6500}}}}}\:\bigstar$

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• Therefore, cost price of the cycle is Rs. 6500.

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$\huge\boxed{\textsf{\textbf{\orange{Know\:More\::-}}}}$

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$\boxed{\begin{array}{c} \\ \tiny\bf{\dag}\:\underline{\frak{\rm{P}\frak{rofit\:and\:loss\:formulas\::-}}} \\\\ \green{\bigstar}\:\rm \red{S.P = \bigg\lgroup\dfrac{100 + Profit\: \%}{100}\bigg\rgroup\: \times \:100 } \\\\ \red{\bigstar}\rm\: \green{ C.P. = \dfrac{S.P \:\times\: 100}{100 + Profit\: \%}}\\\\ \orange{\bigstar}\rm\: \blue{Profit = \dfrac{Profit\: \% \:\times \:C.P}{100}}\\\\ \blue{\bigstar}\rm\: \orange{Profit \:(gain) = S.P - C.P}\\\\ \pink{\bigstar}\rm\: \purple{Profit \:\% = \dfrac{Profit}{C.P} \:\times\: 100} \\\\ \end{array}}$

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