Aptitude - Profit and Loss - Discussion

So in this question Sp is given;

Sp=1920
Sp=1280

Now as per the given question:
percentage profit=percentage loss;
Sp - profit= Sp + loss.
1920-x=1280+x,
2 x=640,
x=320.

And now we have to find Sp at which article was sold.
Sp= (100+(p)%)/100) * C p.
For this we have to find Cp.
C p= Sp - profit.
= 1920-320,
= 1600.

Now we put this CP in to the above formula:

= ((100+25)/100) * 1600.
= (125/100) * 1600,
= 2000.

Thanks @Shubham Singh.

Let c.p=x.
p=1920-x.
l=x-1280.

As we know p% = l%.
1920-x=x-1280.
x=1600.
to get profit 25%.
1600+1600*25%.
----->2000.

In question, they have given that,

The percentage of profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280.

Now profit% = loss%.
From formula profit% = (s.p-c.p/c.p) *100.
Loss% = (c.p-s.p/c.p) *100.

Now equating both from given question,

(s.p-c.p/c.p) * 100 = (c.p-s.p/c.p) *100.

Now by cancelling 100 and c.p.

By substituting s.p values in above formula
1920 - c.p = c.p-1280,
2c.p = 3200.
c.p = 1600.

Now
profit%=(s.p-c.p/c.p) *100,
25=(s.p-1600/1600) *100,
Now after calculation s.p=2000.
Hope this will be helpful.

@All

We can also solve this method:

SP1= 1920 , SP2=1280.
let profit % = loss% = x.

CP1= 100*1920 /(100+x).
CP2= 100*1280 /(100-x).

CP1=CP2
100*1920 /(100+x) = 100*1280 /(100-x)
x=20 = profit% = loss%.

CP= 100*1920 /(100+20) [on putting the value of x].
CP=1600.

New SP= (100+25)*1600 / 100,
New SP=1600.

Explain this question properly.

Easy explanation:

Let C.P=x,
Profit=s.p-c.p
=1920-x
Loss=c.p-s.p
=X-1280.

Then,
Profit%=profit/c.p*100
=((1920-x)/x)*100
Loss%=loss/c.p*100
=((x-1280)/x)*100
Profit%=loss%.

By equating the two,
((1920-x)/x)*100=((x-1280)/x)*100
1920-x=x-1280
2x=3200
x=1600.

Therefore, C.P=1600.
Now,the formula,
S.P=((100+profit%)/100)*C.P.
In que ,profit%=25%.
S.P=((100+25)/100)*1600.
=(125/100)*1600
= 2000.
I hope you all understand.

According to me, the solution is;
1920 - 1280 = 640,
Gain% = loss%,
So, 320=320,
320 + 320 = 640,
CP = 1920 - 320 = 1600,
SP = (1600 * 25/100 + 1600) = 2000.

CP = (1920 + 1280)/2.
= 1600.

SP = (CP+profit).
= [1600 + {1600*(25/100)}],
= 1600 + 400,
= 2000.

since profit(P) and loss(L) percentages are same:
=> P% = L% => P = L .
S.P for P% =1920 ; S.P for L% = 1280
=> 2P =2L = 1920 -1280 = 640
=> P = L = 320
Therefore C.P = S.P(p) - P = S.P(l) + L = 1600

new selling price for 25% profit will be
S.P = ((100 + P) / 100) * C.P = ((100 + 25) / 100) * 1600
= 125/100 * 1600
= 2000