Question

mrs harjeet bought two bags for rs 1150 each. she sold one of them at a gain of 6% and other loss of 2%%. how much did she gain.​

Answer 1

AnswEr :

$\frak{first\:Bag}\begin{cases}\texttt{CP = Rs. 1150}\\\texttt{Gain\% = 6\%}\\\texttt{SP = ?}\end{cases}$

$:\implies\tt SP = CP \times (100+Gain)\%\\\\\\:\implies\tt SP = 1150 \times (100+6)\%\\\\\\:\implies\tt SP =1150 \times 106\%\\\\\\:\implies\tt SP =1150 \times \dfrac{106}{100}\\\\\\:\implies\tt SP =115 \times\dfrac{106}{10}\\\\\\:\implies\tt SP = \dfrac{12190}{10}\\\\\\:\implies\tt SP =Rs.\:1219$

$\rule{150}{1}$

$\frak{second\:Bag}\begin{cases}\texttt{CP = Rs. 1150}\\\texttt{Loss\% = 2\%}\\\texttt{SP = ?}\end{cases}$

$:\implies\tt SP = CP \times (100-Loss)\%\\\\\\:\implies\tt SP = 1150 \times (100-2)\%\\\\\\:\implies\tt SP =1150 \times 98\%\\\\\\:\implies\tt SP =1150 \times \dfrac{98}{100}\\\\\\:\implies\tt SP =115 \times\dfrac{98}{10}\\\\\\:\implies\tt SP = \dfrac{11270}{10}\\\\\\:\implies\tt SP =Rs.\:1127$

$\rule{220}{1}$

$\underline{\bigstar\:\textsf{Total Gain :}}$

$\dashrightarrow\:\:\tt Gain=(Total\:SP - Total\:CP)\\\\\\\dashrightarrow\:\:\tt Gain=\lbrack Rs.(1219+1127)-2(Rs.\:1150)\rbrack\\\\\\\dashrightarrow\:\:\tt Gain= \lbrack Rs. \:2346 - Rs. \:2300 \rbrack\\\\\\\dashrightarrow\:\:\underline{\boxed{\red{\tt Gain= Rs.\:46}}}$

⠀

$\therefore\:\underline{\textsf{Mrs. Harjeet gains \textbf{Rs. 46} on bags.}}$

$\rule{200}{2}$

$\boxed{\begin{minipage}{6.5 cm}\underline{\text{Some Important Formulae Related to it :}}\\ \\ SP=CP\times(100+\sf Profit)\%\\ \\SP=CP\times(100-Loss)\%\\ \\Profit\%=\dfrac{Profit}{CP}\times100 \\ \\Loss\%=\dfrac{Loss}{CP}\times100\end{minipage}}$

Answer 2

Answer:

$\large{\underline{\boxed{\mathfrak\green{She \: gained = Rs.46 }}}}$

Given:-

• CP = 1150 each.
• Gain% in 1st bag = 6%
• Loss% in 2nd bag = 2%

To find:-

• How much she gained?

At first,

• CP = Rs.1150
• Gain% = 6%

$\therefore\rm{Gain = CP \times Gain\%} \\\\\Rightarrow\rm{Gain = 1150 \times 6\%} \\\\\therefore\rm Gain = {\boxed{\text{Rs.69 }}}$

$\rm We \: know, \\\\\star\: {\boxed{\text{SP = CP + Gain }}}$

$\: \: \: \: \dag\text{Substituting \: values :- }$

$\Rightarrow\rm SP_1 =Rs. (1150 + 69) \\\\\Rightarrow\rm SP_1 = {\boxed{\bf\green{Rs.1219 }}}$

$\rule{100}{1}$

Secondly,

• CP = Rs.1150
• Loss% = 2%

$\rm We \: know, \\\\\star \: {\boxed{\bf\blue{SP = CP - Loss}}}$

$\: \: \: \: \dag\text{Substituting \: values:- }$

$\Rightarrow\rm SP_2 = 1150 - (1150 \times 2\%) \\\\\Rightarrow\rm SP =Rs.( 1150 - 23 ) \\\\\Rightarrow\rm SP_2 ={\boxed{\bf\red{Rs.1127 }}}$

$\rule{200}{2}$

$\rm We \: know, \\\\\star \: {\boxed{\bf\blue{Total \:gain = Total \:SP - Total \: CP }}}$

$\: \: \: \: \: \dag\text{Substituting \: values :- }$

$\Rightarrow\rm Total \: gain =( SP_1 + SP_2 ) - (CP_1 + CP_1) \\\\\Rightarrow\rm Total \: gain = (1219 + 1127) - (1150 + 1150) \\\\\Rightarrow\rm Total \: gain =Rs. (2346 - 2300) \\\\\Rightarrow\rm Total \: gain = {\boxed{\bf\purple{Rs.46 }}}$

${\underline{\underline{\therefore{\text{She \: overall \: gained \: Rs.46 . }}}}}$