Aptitude - Profit and Loss - Discussion

@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!!

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.

When we assume C.P is 100,

Given % = ((S.P-C.P)/C.P)*100.

25 = (S.P-X)/X)*100.

25/100 = (S.P- X)/X.

Now substitute X = 100.

You will get S.P = 125.

Similarly,

If the gain % 55, S.P = 155.

If the gain % 65, S.P = 165.

If the gain % 75, S.P = 175.

Same way for loss % = ((C.P-S.P)/C.P)*100.

If you get loss % = 75, S.P = 25.

Check with assuming C.P= 100, since 100 easy to calculate.

If loss = 25, S.P =75.

Also check the important facts in: http://www.indiabix.com/aptitude/profit-and-loss/formulas.

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.

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

No need to worry, first understand the question carefully,given only selling prices,not given cost prices,first we find cost price.

From selling price 1280 .
I find out the cost price.see profit is 25%.
C.p = 1600 [10% of 1280 = 128,
5%=64, 10% + 10% + 10% = 25%,
i.e128 + 128 + 64 = 320.

Add 1280 + 320 = 1600(or) 1920 - 320=1600
Now S.p = 1600 * 125/100 = 2000.

[To get 25% out of 1600 is 125 . profit add 100, 100 + 25 = 125, loss subtract from 100, 100 - 25 = 75].

It is very simple question.

At first,

First article cp = x.
second article cp = x.
Total-------------------------
= 2x.

First article sp =1920.
Second article sp= 1280.
Total-----------------------
= 3200.

Then first article cp = 3200/2 = 1600.

According to the question.
Get 25% profit.

100 is = 125.
1 is = 125/100.

1600 is = 125/100*1600.
= 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

Given :
Selling price with profit = 1920/-
Selling price with loss= 1280/
1920 - 1280 =640
RS.640 is loss.

Here Profit==Loss
So,
Half the amount is profit . that is RS.320/- ]

Cost price =selling price-profit.
= 1920 - 320,
=> 1600/
-
What is 25% in 1600/-
25/100 * 1600 = 400.

cp + profit(25%) = sp.
then, 1600+400 = 2000/- that is the selling price with 25%..

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.