A merchant purchased a Wrist watch for Rs.450 and fixed its list price

1.	A merchant purchased a Wrist watch for Rs.450 and fixed its list price in such a way that after allowing a discount of 10%,he earns a profit of 20%,Find the list price of the wrist watch?
Answer» ong>Step-by-step explanation: $\bf\underline{\underline{\red{Given:-}}}$ A merchant purchased a Wrist WATCH for Rs.450. After ALLOWING a discount of 10%,he earns a profit of 20%. $\bf\underline{\underline{\blue{To\:Find:-}}}$ The LIST price of the wrist watch. $\bf\underline{\underline{\green{Solution:-}}}$ $\rm Let\: the\: list \: price \: of\: the \: watch \: be\: Rs. x$ $\rm Discount \% = 10\%$ $\rm Discount = \dfrac{10}{100}\times list\: price$ $\rm = \dfrac{10}{100}\times x$ $\rm= \dfrac{x}{10}$ $\rm \dashrightarrow Discount = \dfrac{x}{10}$ $\rm Selling\: price = List\: price - Discount$ $\rm = x - \dfrac{x}{10}$ $\rm = \dfrac{ 10x - x}{10}$ $\rm = \dfrac{ 9x}{10}$ $\rm \dashrightarrow \underline{\: \: \underline{\: Selling\: price= \dfrac{9x}{10}\: }\: \:}$ $\rm Now,\: Given\: Cost \: Price \: (CP) = Rs.450$ $\rm Profit\%= 20\%$ $\rm \leadsto Selling \: price = \dfrac{ 100 + Profit\%}{100}\times CP$ $\rm \implies \dfrac{9x}{10}= \dfrac{ 100 + 20}{100}\times 450$ $\rm\implies \dfrac{9x}{10} = \dfrac{ 120}{100}\times 450$ $\rm\implies \dfrac{9x}{10}= 12 \times 45$ $\rm\implies \dfrac{9x}{10}= 540$ $\rm\implies x= 540\times \dfrac{10}{9}$ $\rm\implies x = 600$ $\rm List\: price = x = Rs. 600$ $\underline{\boxed{\purple{\rm \therefore List\: price\: of \: the\: watch = Rs.600}}}$