Gill won certain prize money in a cooking competition. She spent half price money on clothes and one third on crockery and gave the remaining 2000 rupees an orphanage. how much money did she win?


Given:  Gill won a cooking competition.

$\frac{1}{2}$ spent on clothes

$\frac{1}{3}$ spent on crockery

Rs 2000  donated in to orphanage

To do:  Find the prize money won by her. 


Solution:


Lets take the prize money won   =Rs  $x$ 

Half the prize money spent on clothes, 

Money spent on clothes  =  Rs$\frac{ x}{2}$ 

one third of prize money spent on crockery,

Money spent on crockery  =   Rs$\frac{x}{3} $

Money given to orphanage =  Rs 2000 

Total prize money  =  Money spent on clothes  $+$  Money spent on crockery   $+$  Money given to orphanage

 

 $x = \frac{ x }{ 2}   +  \frac{ x}{ 3 }  +   2000$

Now bring all variables(x) on the same side,

 $ x  -  \frac{x }{ 2}   -  \frac{x }{ 3}    =   2000$

Denominators are different,

to make them equal , take  LCM

LCM of 2 , 3 is  6

$\frac{x \times 6  }{  1 \times 6}  =  \frac{6 x }{ 6}$

$\frac{x \times 3  }{  2 \times 3}  =  \frac{3 x }{ 6}$

$\frac{x \times 2  }{  3 \times 2}  = \frac{2 x }{ 6}$

 

$\frac{6 x }{ 6}-\frac{3 x }{ 6}-\frac{2 x }{ 6}$ =2000

$\frac{6x-3x2x}{6}$=2000

$\frac{x}{6} =2000$

$x= 2000\times 6$

$x= 12000 $


Therefore, Gill won Rs 12000

                       


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Updated on: 10-Oct-2022

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