Question

Paro purchased two ceiling fans for 1,000 each. She sold one of them at a loss of 10%. At what price should the other be sold so as to gain 20% on the whole transaction?
(Step by step explanation)​

Answer 1

$\large \purple{ \underline{ \mathtt{ \red{ given : }}}} \\ \\ \large \mathtt{cost \: \: price = rs.1000} \\ \\ \large \mathtt{loss \: \: percent= 10\%} \\ \\ \large \mathtt{findng \: \: selling \: \: price}$

$\large \pink{ \underline{ \mathtt{ \green{ using \: \: formula: }}}} \\ \\ \boxed{\large \mathtt{s.p = c.p \times \left(\frac{100 - l\%}{100} \right)} }$

${\large: \implies\mathtt{s.p = 1000 \times \left( \frac{100 - 10}{100} \right)} } \\ \\ \\ {\large: \implies\mathtt{s.p = 1000 \times \left( \frac{90}{100} \right)} } \\ \\\\ {\large: \implies\mathtt{s.p = 1000 \times \left( \frac{9 \cancel0}{100 \cancel0} \right)} } \\ \\ \\ {\large: \implies\mathtt{s.p = 1000 \times \left( \frac{9}{10} \right)} } \\ \\ \\ {\large: \implies\mathtt{s.p = 100 \cancel0 \times \left( \frac{9}{1 \cancel0} \right)} } \\ \\ \\ {\large: \implies\mathtt{s.p = 100\times {9} } } \\ \\ \\ {\large \therefore \: \underline{ \underline{\mathtt{ \blue{s.p} = \green{r.s \: \: 90 0 }}} }}$

$\large \mathtt{let \: \: s.p \: \: of \: \: fan \: = c.p} \\ \\ \large \mathtt{so. \: \: } \\ \\ \large \mathtt{s.p = 1000 + 900 = rs \: 1900} \\ \\ \large \mathtt{c.p = 1000 + 1000 = rs \: 2000} \\ \\ \large \mathtt{loss = rs \: 100} \\ \\ \large \mathtt{profit \: \% = 20\%}$

$\large \pink{ \underline{ \mathtt{ \orange{ using \: \: formula: }}}} \\ \\ \boxed{\large \mathtt{profit = \frac{profit\% \times c.p}{100} } }$

$\large \mathtt{ : \implies \: p = \dfrac{20 \times 200}{100} } \\ \\ \\ \large \mathtt{ : \implies \: p = \dfrac{20 \times 20 \cancel{00}}{1 \cancel{00}} } \\ \\ \\ \large \mathtt{ : \implies \: p = {20 \times 20} } \\ \\ \\ \boxed{\large \mathtt{ \therefore \: profit = rs \: 400} }$

Selling price = 1900 + 400 = rs 2300