Question

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

need answer in process
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Answer 1

GIVEN :-

• A shopkeeper sold two watches for Rs. 920 each.

TO FIND :-

• His profit or loss %.

SOLUTION :-

$\underline{ \bigstar \: \textsf{Situation \: 1.}}$

$\bullet \displaystyle \sf \: S.P = Rs. 920$

$\bullet \displaystyle \sf \: profit \: \% = 15$

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

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

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

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

$\underline{ \bigstar \: \textsf{Situation \: 2.}}$

$\bullet \displaystyle \sf \: S.P = Rs. 920$

$\bullet \displaystyle \sf \: loss \: \% = 60$

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

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

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

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

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

_______________…

$\\ \dashrightarrow\displaystyle \sf \:total \: C.P = 2300 + 800$

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

Now,

$\\ \dashrightarrow\displaystyle \sf \:total \: S.P = 920 + 920$

$\dashrightarrow \underline{ \boxed{\displaystyle \sf \:total \: S.P = 1840}}$

______________…

$\\ : \implies \displaystyle \sf \: S.P < C.P$

$: \implies \displaystyle \sf \:loss \: = C.P - S.P$

$: \implies \displaystyle \sf \:loss = 3100 - 1840$

$: \implies\underline{ \boxed{\displaystyle \sf \:loss = 1260}}$

Now,

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

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

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

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

Answer 2

${\boxed{\underline{\tt{ \orange{Required \: \: Answer:-}}}}}$

★GIVEN:-

• A shopkeeper sold two eatches at Rs. 920.

• At one watch profit % is 15%

• At another watch loss % is 60%

★TO FIND :-

• his profit or loss percent.

★SOLUTION:-

1st CASE:-

$: \implies \: \tt{S.P.\: = \:Rs. \:920}$

$: \implies\tt{Profit\% = 15\%}$

$: \implies \: \tt{C.P. = \frac{s.p. \times 100}{100 + p\%}}$

$: \implies \: \tt{C.P.\: =\: \frac{920×100}{100+15}}$

$: \implies \: \tt{C.P. \: =\: \frac{92000}{115}}$

$: \implies \: \tt{C.P.\:=\: Rs.800}$

2nd CASE:-

$: \implies \: \tt{S.P.\:=\:Rs.\:920}$

$: \implies \: \tt{Loss\% = 60\%}$

$: \implies \: \tt{C.P. = \frac{s.p. \times 100}{100 - loss\%}}$

$: \implies \: \tt{C.P. \: = \: \frac{920×100}{100-60}}$

$: \implies \: \tt{C.P. \: = \: \frac{92000}{40}}$

$: \implies \: \tt{C.P. \: = \: \frac{1200}{4}}$

$: \implies \: \tt{C.P.\:=\: Rs.300}$

_______________________________________________★

TOTAL C.P. = 2300 + 800

$: \implies \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {\boxed{\underline{\tt{TOTAL \: \: C.P. = Rs.\:\:3100}}}}$

TOTAL S.P. = 920 + 920

$: \implies \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {\boxed{\underline{\tt{TOTAL \: \: S.P. = Rs.\:\:1840}}}}$

SO,

S.P. < C.P.

Loss = 3100 - 1840

$: \implies \: {\boxed{\underline{\tt{loss = Rs.\:\:1260}}}}$

$: \implies \: \tt{Loss\% = \frac{loss}{C.P} \times 100}$

$: \implies \: \tt{Loss\% = \frac{1260}{3100} \times 100}$

$: \implies \: \tt{Loss\% = \frac{12600}{31}}$

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

HOPE IT HELPS