Question

Bhawna bought two fans for 3605. She sold one at a profit of 15% and the other at a loss of 9°/•.
If Bhawna obtained the same amount for each fan, find the cost price of each fan.
​

Answer 1

$\bf \red{ \underline{ \underline{solution}}}$

Let C.P of first fan= x

Then C.P of second fan = Rupees (3605-x)

• For the sale of first fan,profit=15°/•

$sp \: offirst \: fan = \purple {\frac{100 + profit\%}{100} \times cp}$

$= ( \frac{100 + 15}{100}) \times x$

$= \frac{115x}{100}$

• For sale of second fan,loss=9°/•

$sp \: of \: 2nd \: fan = \blue { \frac{100 - loss\%}{100} \times cp}$

$= ( \frac{100 - 9}{100} ) \times( 3605 - x)$

$= \frac{91(3605 - x)}{100}$

By the given conditions

S.P of first fan=S.P of Second fan

$= > \: \frac{115x}{100} = \frac{19(3605 - x)}{100}$

$= > 115x = 91(3605 - x)$

$= > 115x = 91 \times 3605 - 91x$

$= > 115x + 91x = 91 \times 3605$

$= > 206x = 91 \times 3605$

$= > x = \frac{91 \times 3605}{206}$

$= > x = \frac{91 \times 35}{2}$

$= > x = \frac{3185}{2}$

$=> x = 1592.50$

$\blue{\therefore cp \: of \: first \: fan} = > x = \bold{1592.50}$

$\: cp \: of \: 2nd \: fan = > 3605 - x$

$= > 3605 - 1592.50$

$\: = > \bold{2012.50}$

Answer 2

AnswEr :

$\bf{\green{\underline{\underline{\bf{Given\::}}}}}$

Bhawna bought two fans for Rs.3605. She sold one of at a profit of 15% and other at a loss of 9%. If Bhawna obtained the same amount for each fan.

$\bf{\red{\underline{\underline{\bf{To\:find\::}}}}}$

The cost price of each fan.

$\bf{\purple{\underline{\underline{\bf{Explanation\::}}}}}$

Let the 1st fan of cost price be Rs.R

Let the 2nd fan of cost price be Rs.M

So,

$\leadsto\tt{R+M=3605}\\\\\leadsto\tt{\pink{M=3605-R...........................(1)}}$

$\dag\bf{\underline{\underline{\bf{Selling\:price\:(S.P.)\:of\:1st\:fan\::}}}}}}$

$\mapsto\sf{S.P.=\dfrac{100+profit\%}{100} \times C.P.}\\\\\\\\\mapsto\sf{S.P.=\dfrac{100+15}{100} \times R}\\\\\\\\\mapsto\sf{S.P.=\dfrac{115}{100} \times R}\\\\\\\\\mapsto\sf{\purple{S.P.=\dfrac{115R}{100} }}$

$\dag\bf{\underline{\underline{\bf{Selling\:price\:(S.P.)\:of\:2nd\:fan\::}}}}}}$

$\mapsto\sf{S.P.=\dfrac{100-loss\%}{100} \times C.P.}\\\\\\\\\mapsto\sf{S.P.=\dfrac{100-9}{100} \times M}\\\\\\\\\mapsto\sf{S.P.=\dfrac{91}{100} \times M}\\\\\\\\\mapsto\sf{\purple{S.P.=\dfrac{91M}{100} }}$

$\bf{\red{\underline{\underline{\tt{According\:to\:the\:question\::}}}}}$

$\Rightarrow\tt{\dfrac{115R}{\cancel{100}} =\dfrac{91M}{\cancel{100}} }\\\\\\\Rightarrow\tt{115R=91M}\\\\\\\Rightarrow\tt{115R=91(3605-R)\:\:\:\:\:\:\big[from(1)\big]}\\\\\\\Rightarrow\tt{115R=328055-91R}\\\\\\\Rightarrow\tt{115R+91R=328055}\\\\\\\Rightarrow\tt{206R=328055}\\\\\\\Rightarrow\tt{R=\cancel{\dfrac{328055}{206} }}\\\\\\\Rightarrow\tt{\purple{R\:=\:Rs.1592.5}}$

Putting the value of R in equation (1), we get;

$\leadsto\tt{M=Rs.(3605-1592.5)}\\\\\leadsto\tt{\purple{M=Rs.2012.5}}$

Thus,

$\underbrace{\sf{The\:cost\:price\:(C.P.)\:of\:1st\:fan\:=\:Rs.1592.5}}}}\\\\\underbrace{\sf{The\:cost\:price\:(C.P.)\:of\:2nd\:fan\:=\:Rs.2012.5}}}}}$