Question

QUESTION:-
Abha bought 2 calculators at Rs 900. She sold one at profit of 20% and other at a loss of 20%. If the SP of both calculator was same, then find the CP of each calculator.
SUBJECT : Maths
TOPIC : Profit or Loss
CLASS : 8th​

Answer 1

$\large \dag$ Question :-

Abha bought 2 calculators at Rs 900. She sold one at profit of 20% and other at a loss of 20%. If the SP of both calculator was same, then find the CP of each calculator.

$\large \dag$ Answer :-

$\red\dashrightarrow\underline{\underline{\sf  \green{CP \:  of  \: First \:  Calculator=Rs\:360}} }$

$\red\dashrightarrow\underline{\underline{\sf  \green{CP \:  of  \: Second \:  Calculator=Rs\:540}} }$

$\large \dag$ Important Formulas :-

$\bf \red\bigstar \: \: \orange{ \underbrace{ \underline{ SP = \frac{100 - Lost\%}{100} \times CP}}}$

$\bf \red\bigstar \: \: \orange{ \underbrace{ \underline{ SP = \frac{100 + Gain\%}{100} \times CP}}}$

$\large \dag$ Step by step Explanation :-

Let us Assume that,

▪ Cost Price of 1st Calculator = Rs $\large \bf x$

⇝ As She bought the 2 calculators at Rs 900

Therefore,

▪ Cost Price of 2nd Calculator = Rs $\large \bf (900-x)$

Now,

❒ Calculating Selling Price of 1st Calculator :-

According to the Given Condition 1st Calculator is sold at profit of 20 %.

Therefore Selling Price of 1st Calculator is :

$\rm \: \: \: SP_1 = \frac{100 + 20}{100} = x$

$:\longmapsto \rm SP_1 = \frac{120}{100} \times x$

$\purple{ \large :\longmapsto  \underline {\boxed{{\bf SP_1 = \frac{6x}{5} } }}}$

❒ Calculating Selling Price of 2nd Calculator :-

According to the Given Condition 2nd Calculator is sold at loss of 20 %.

Therefore Selling Price of 2nd Calculator is :

$\rm \: \: \: SP_2 = \frac{100 - 20}{100} \times (900-x)$

$:\longmapsto \rm SP_2 = \frac{80}{100} \times (900-x)$

$:\longmapsto \rm SP_2 = \frac{4}{5} \times (900 - x)$

$\purple{ \large :\longmapsto  \underline {\boxed{{\bf SP_2 = \frac{3600-4x}{5} } }}}$

$\large \blue \bigstar$ As per the Question the selling price for both calculators is same :

$\large:\longmapsto \underline{ \overline{{\boxed{ \rm SP_1=SP_2}}}}$

⏩ Putting Values of Both ;

$:\longmapsto \rm \frac{6x}{ \cancel5} = \frac{3600 - 4x}{\cancel5}$

$:\longmapsto \rm 6x = 3600 - 4x$

$:\longmapsto \rm 6x + 4x = 3600$

$:\longmapsto \rm 10x = 3600$

$:\longmapsto \rm x = \cancel \frac{3600}{10}$

$\purple{ \Large :\longmapsto  \underline {\boxed{{\bf x = 360} }}}$

$\red\dashrightarrow\underline{\underline{\sf  \green{CP \:  of  \: First \:  Calculator=Rs\:360}} }$

As Abha bought 2 calculators at Rs 900.

$\small\therefore \text{\sf CP of 2nd Calculator = 900 - \rm x }$

$:\longmapsto\small \text{\sf CP of 2nd Calculator = 900 - \rm 360 }$

$\red\dashrightarrow\underline{\underline{\sf  \green{CP \:  of  \: Second \:  Calculator=Rs\:540}} }$

Answer 2

G I V E N :

Abha bought 2 calculators at Rs 900. She sold one at profit of 20% and other at a loss of 20%. If the SP of both calculator was same, then find the CP of each calculator.

S O L U T I O N :

Let us assume the Cost Price of the Calculator be a

As the cost of both the calculators is ₹900

Thereby, Cost of the other calculator be 900 - a

Here, we will assume 100% as a point like zero

Now, as the first calculator suffered a loss of 20%

So, it should be 100% - 20% = 80%

$\sf Selling \: Price \: of \: the \: calculator = \frak{a \times 80\%} \\ \\ \sf Selling \: Price = \frak{a \times \frac{80}{100} } \implies {\frak{ \frac{80}{100}a}} \implies \frak{ \green{ \frac{8}{10}a }}$

Now, for the another calculator

It gained a profit of 20%

$\sf Selling \: Price \: of \: another \: calculator = \frak{a \times 120\%} \\ \\ \sf Selling \: Price = \frak{a \times \frac{120}{100} } \implies {\frak{ \frac{120}{100}a}} \implies \frak{ \purple{\frac{12}{10}(900 - a)}}$

Now, a clue is provided that Selling Price of both the calculator are same

$\sf Selling \: Price \: of \: first \: calculator = Selling \: Price \: of \: the \: other \: one \\ \\ \rightharpoonup\frak{ \frac{8}{10}a = \frac{12}{10}(900 - a)} \\ \\ \rightharpoonup \frak{ \frac{8}{10}a \times \frac{10}{12} = 900 - a } \\ \\ \rightharpoonup \frak{ \frac{8}{12}a = 900 - a } \\ \\ \rightharpoonup \frak{ \frac{2}{3}a = 900 - a } \\ \\ \rightharpoonup\frak{2a = 3(900 - a)} \\ \\ \rightharpoonup\frak{2a = 2700 - 3a} \\ \\ \rightharpoonup\frak{5a = 2700} \\ \\ \rightharpoonup\frak{a = \frac{2700}{5} } \\ \\ \rightharpoonup\frak{a = \cancel\frac{2700}{5} } \\ \\ \star \quad \underline{ \boxed{ \frak{a = 540}}}$

$\bigstar \: \: \underline{\frak{Finding \: {\sf P}rice }} :$

$\odot\quad\frak{First \: Calculator = a = \blue{900}} \\ \\ \odot\quad\frak{Other \: Calculator = 900-a = 900-540= \blue{360}}</p><p>$