Question

A shopkeeper sold two watches for Rs. 920 each. On one watch he gained 15% and on the other he lost 60%. Find his profit or loss percent.​

Answer 1

GIVEN :-

A shopkeeper sold two watches for Rs. 920 each.

TO FIND :-

His profit or loss %.

SOLUTION :-

$\begin{gathered} \underline{ \bigstar \: \textsf{Situation \: 1.}} \\ \\ \end{gathered}$

$\begin{gathered} \bullet \displaystyle \sf \: S.P = Rs. 920 \\ \\ \end{gathered}$

$\begin{gathered}\bullet \displaystyle \sf \: profit \: \% = 15 \\ \\ \end{gathered}$

$\begin{gathered} : \implies\displaystyle \sf \: C.P = \frac{S.P \times 100}{100 + profit \: \%} \\ \\ \\ \end{gathered}$

$\begin{gathered}: \implies\displaystyle \sf \: C.P \: = \frac{920 \times 100}{100 + 15} \\ \\ \\ \end{gathered}$

$\begin{gathered}: \implies\displaystyle \sf \: C.P \: = \frac{92000}{115} \\ \\ \\ \end{gathered}$

$\begin{gathered}: \implies \underline{ \boxed{\displaystyle \sf \: C.P \: = Rs. \: 800}} \\ \\ \end{gathered}$

$\begin{gathered}\underline{ \bigstar \: \textsf{Situation \: 2.}} \\ \\ \end{gathered}$

$\begin{gathered}\bullet \displaystyle \sf \: S.P = Rs. 920 \\ \\ \end{gathered}$

$\begin{gathered}\bullet \displaystyle \sf \: loss \: \% = 60 \\ \\ \end{gathered}$

$\begin{gathered}: \implies\displaystyle \sf \: C.P = \frac{S.P \times 100}{100 - loss \: \%} \\ \\ \\ \end{gathered}$

$\begin{gathered}: \implies\displaystyle \sf \: C.P \: = \frac{920 \times 100}{100 - 60} \\ \\ \\ \end{gathered}$

$\begin{gathered}: \implies\displaystyle \sf \: C.P \: = \frac{92000}{40} \\ \\ \\ \end{gathered}$

$\begin{gathered}: \implies\displaystyle \sf \: C.P = \frac{9200}{4} \\ \\ \\ \end{gathered}$

$\begin{gathered}: \implies \underline{ \boxed{\displaystyle \sf \: C.P \: = 2300}} \\ \\ \end{gathered}$

$\begin{gathered} \\ \dashrightarrow\displaystyle \sf \:total \: C.P = 2300 + 800 \\ \\ \\ \end{gathered}$

$\begin{gathered}\dashrightarrow \underline{ \boxed{\displaystyle \sf \:total \: C.P = 3100}} \\ \\ \end{gathered}$

Now,

$\begin{gathered} \\ \dashrightarrow\displaystyle \sf \:total \: S.P = 920 + 920 \\ \\ \\ \end{gathered}$

$\begin{gathered}\dashrightarrow \underline{ \boxed{\displaystyle \sf \:total \: S.P = 1840}} \\ \\ \end{gathered} </p><p>$

$\begin{gathered}: \implies \displaystyle \sf \:loss \: = C.P - S.P \\ \\ \\ \end{gathered}$

$\begin{gathered} : \implies \displaystyle \sf \:loss = 3100 - 1840 \\ \\ \\ \end{gathered}$

Now,

$\begin{gathered} \\ : \implies \displaystyle \sf \:loss \: \% = \frac{loss}{C.P} \times 100 \\ \\ \\ \end{gathered}$

$\begin{gathered} : \implies \displaystyle \sf \:loss \: \% = \frac{1260}{3100} \times 100 \\ \\ \\ \end{gathered}$

$\begin{gathered} : \implies \displaystyle \sf \:loss \: \% = \frac{1260}{31} \\ \\ \\ \end{gathered}$

$: \implies \underline{ \boxed{ \displaystyle \sf \:loss \: \% = 40.64}}$