Aptitude - Profit and Loss - Discussion

Why 125%? Please explain.

1920 + 1280 ÷ 2.
1600 than 25%.
1600 * 5/4 = 2000.

Hello, guys for clear govt. The exam follows these steps:
Cp = average of both selling price (because gap is same)
= 1600.
New sp = 1600 * 5/4 = 2000(ans).

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

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

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

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.

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.

Explain this question properly.

@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.

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.