Aptitude - Profit and Loss - Discussion

What formula is used and in question it is 25% in answer it is shown as 125% please explain

@sunitha: do the step untill x=1600, then you can calculate 25% profit for cp 1600, if you calculate then you get Rs-400 then add that with 1600, you will get Rs-2000 (1600+400) because they ask overall amount for 25% so they calculate 125% (100+25).

How the x value is find?

@kumar::

In the first case, by selling d article we get profit.so,the formula for gain=s.p-c.p
here we consider c.p as 'x'(cos its not gvn in quest)
therefore gain=1920-x
gain%=gain*100/(c.p)
so we get, gain%=(1920-x)*100/(x)

In the second case, by selling the product we get loss. so,the formula for loss= c.p-s.p

as we know, c.p=x(assumption)
s.p=1280
loss=x-1280

we need to find loss% here.. the formula is
loss%=loss*100/(c.p)

so we get, loss%=(x-1280)*100/(x)

as both the articles are same products we are equating both.

(1920-x)*100/(x)=(x-1280)*100/(x)
1920 - x = x - 1280

2x = 3200

x = 1600

hope you understood..! happy day!!

profit=loss=x
sp1=1920
sp2=1280

sp-profit=sp+less
1920-X=1280+x
2x=640
x=320

cp=sp-profit
=1920-320=1600

new sp=1600*125/100
=2000

How 125 arrive?

Its very simple questions profit incrd when selng it at 1920 is same as los when sel it at 1280 take average of two .i.e .1920+1280/2=1600 is new cost so prf 25%of 1600=400.so add 1600+400=2000

1920+1280/2=1600
25%of 1600=400
1600+400=2000

Its Simple, we have to use Gain% formula, see

Gain% = Gain*100/CP or SP-CP *100/CP
Let CP = x, then

case I = 1920 - x *100/x
case II = x - 1280*100/x [here i use loss% formula]
Now, compare the two cases, we get
1920 - x*100/x = x -1280*100/x
or 1920x - x^2 = x^2 - 1280
or 1920x - x^2 - x^2 + 1280 = 0
or 3200x - 2x^2 = 0
or 3200 = 2x
x = 1600 = CP
Now, use SP formula
S.P = 1 + Gain% * CP
1 + 25/100 * 1600
125/100 *1600
= 2000

We have to calculate s.p
so formula is,
s.p=(100+profit%)*c.p/100.............(1)
now look at formula
we have profit % only we have to calculate c.p
now read our problem
assume,
profit=loss=x
sp1=1920
sp2=1280

sp1-x=sp2+x
1920-x=1280+x
1920-1280=2x
640=2x
x=320
Now we have formula to calculate c.p
c.p=s.p-profit...........................(2)
c.p=1920-320
c.p=1600
now put values in formula(1)
we get,
s.p=(100+25)*1600/100
s.p=125*1600/100
s.p=2000

Therefore selling price is 2000 to earn 25% profit