Question

By selling two chairs for Rs.1200 each, a man gains 10% on one chair & loses 10% on the other . Find his gain or loss per cent in the whole transaction.

Answer 1

@satellite73 @Zarkon Plz help :)

Answer 2

He gains 120, but as well as losses 120

Answer 3

i guess we can do it with the numbers given. so the 1200 is a ten percent gain, meaning if i read it correctly that it is 110% what the chair cost the merchant
the merchant therefore pain \(1200\div1.1=1090.91\) rounded for the chair, and made a profit of \(\$109.09\)

Answer 4

ya i also did something like that but not getting the concept :(

Answer 5

similarly the other 12000 represented at 10% loss, so he sold it for 90% of his cost
his cost was therefore \(1200\div .9=1333.33\) rounded and he lost 133.33

Answer 6

hmm...

i solved this through right here only

Answer 7

what is the next step ?

Answer 8

then the net loss is \(109.09-133.33=-24.24\)

Answer 9

yes !

Answer 10

as a percent of the entire transaction it is
\[-\frac{24.24}{2400}\]

Answer 11

ok

Answer 12

usually it is easier to work with numbers but this time it might be easier to work with variables

Answer 13

yup!

Answer 14

\[\frac{\frac{x}{1.1}-\frac{x}{.9}}{2x}\]

Answer 15

oh wait that is not right, let me try again

Answer 16

okay!

Answer 17

if we replace \(1200\) by \(x\) it looks like we computed
\[\frac{\frac{x}{1.1}-x+\frac{x}{.9}-x}{2x}\]

Answer 18

now maybe some algebra to clean it up
looks like we get
\[\frac{1}{99}\]

Answer 19

why ?

Answer 20

actually it is the other way around \[\frac{x-\frac{x}{1.1}+x-\frac{x}{.9}}{2x}\]

Answer 21

why as in how did i get \(\frac{1}{99}\)?

Answer 22

multiply top and bottom by either 9.9 or 99 to clear the decimal, combine like terms etc and you will get it
\(\frac{1}{99}=.010101...\) as a prercent it is a loss of \(1\%\) rounded, but really \(1\tfrac{1}{99}\%\)

Answer 23

hmmmmm..

I see thanx :)

Answer 24

yw