Profit & Loss

[nikita27]

Question:

A trader buys a number of lemons at the rate of 7 for $1 and an equal number of lemons at the rate of 5 for $1. He mixed them and sells the entire lot at the rate of 6 for $1. What his loss% or gain%?

Options:
i) No Loss or Gain
ii) 2.78% loss
iii) 2.33% loss
iv) 1.67% loss
E) None of these

[spoiler]2.78%[/spoiler]

[nikita27]

I found two solutions:

1st Solution:

Let the merchant buy 210 lemons (LCM of 5,6,7) of the first variety and 210 for the 2nd variety.
His cost = 30 + 42 = 72
He sells the entire lot of 420@6.
Therefore, his SP = 70, Loss = 2, CP = 72
Therefore, %LOSS = 2.78%

2nd solution:

Ist Variety: 7 lemons ----- $1
IIn Variety: 5 lemons ----- $1
-----------------------------------
CP Mixture: 12 lemons ----- $2
-----------------------------------
SP Mixture: 6 lemons ----- $1
===> 12 lemons ----- $2

Hence, No Profit No Loss.

Now, I am confused how do we have two different solutions.

Help?

[xcusemeplz2009]

let x be the no. of lemons

amount paid for x lemons @1/7 = x/7
amnt paid for same x lemons @ 1/5=x/5

tot paid=x/7+x/5=12x/35

SP for 2x lemons @ 1/6=2x/6=x/3

loss= 12x/35-x/3=x/(35*3)
% loss=[[x/(35*3)]/12x/35]*100=2.77%

hence B

[xcusemeplz2009]

I found two solutions:

1st Solution:

Let the merchant buy 210 lemons (LCM of 5,6,7) of the first variety and 210 for the 2nd variety.
His cost = 30 + 42 = 72
He sells the entire lot of 420@6.
Therefore, his SP = 70, Loss = 2, CP = 72
Therefore, %LOSS = 2.78%

2nd solution:

Ist Variety: 7 lemons ----- $1
IIn Variety: 5 lemons ----- $1-----------------------------------
CP Mixture: 12 lemons ----- $2
-----------------------------------
SP Mixture: 6 lemons ----- $1
===> 12 lemons ----- $2

Hence, No Profit No Loss.

Now, I am confused how do we have two different solutions.

Help?

the problem in the secon case is you are buying different no. of lemmons for both the cases
rephrasing it

7 lemmons..........1$
5 L......1$=>7 L costs....7/5$( we are given a condition of equal no. of lemmons)
...............................
CP mixture 1+7/5=12/5
...............................
SP mixture
6L.........1$
14 L.......14/6=7/3

loss=12/5- 7/3=1/15
%loss={1/15}*100/{12/5}=100/36=2.78%