Question

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 1

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.

$\bf\underline{\underline{\green{Solution:-}}}$

$\rm Let\: the\: list \: price \: of\: the \: watch \: be\: Rs. x$

$\rm Discount \% = 10\%$

$\rm Discount = \dfrac{10}{100}\times list\: price$

$\rm = \dfrac{10}{100}\times x$

$\rm= \dfrac{x}{10}$

$\rm \dashrightarrow Discount = \dfrac{x}{10}$

$\rm Selling\: price = List\: price - Discount$

$\rm = x - \dfrac{x}{10}$

$\rm = \dfrac{ 10x - x}{10}$

$\rm = \dfrac{ 9x}{10}$

$\rm \dashrightarrow \underline{\: \: \underline{\: Selling\: price= \dfrac{9x}{10}\: }\: \:}$

$\rm Now,\: Given\: Cost \: Price \: (CP) = Rs.450$

$\rm Profit\%= 20\%$

$\rm \leadsto Selling \: price = \dfrac{ 100 + Profit\%}{100}\times CP$

$\rm \implies \dfrac{9x}{10}= \dfrac{ 100 + 20}{100}\times 450$

$\rm\implies \dfrac{9x}{10} = \dfrac{ 120}{100}\times 450$

$\rm\implies \dfrac{9x}{10}= 12 \times 45$

$\rm\implies \dfrac{9x}{10}= 540$

$\rm\implies x= 540\times \dfrac{10}{9}$

$\rm\implies x = 600$

$\rm List\: price = x = Rs. 600$

$\underline{\boxed{\purple{\rm \therefore List\: price\: of \: the\: watch = Rs.600}}}$