Aptitude - Profit and Loss - Discussion

Guys,
It's simple.

For example
Sp =rs100,
Sp =rs110.

Now, Sp is doubled.

(ie) :sp=2(110) rs=>220 but remember cp remains the same.

Then, we know.
1) profit=sp-cp
2) profit %= (sp-cp/cp)100.

From the question;

If Sp is doubled the profit triple so with this we build the equation.

2sp-cp = 3(profit).
(ie)
2sp-cp=3(sp-cp).

We get
Sp=2cp ---> (1)

To find profit %
(Sp-cp/cp) 100.

Sub 1 in the formula above;

(2cp-cp/cp)100.

So, finally, we get 100%.

We know that profit = SP - CP.
Let SP - CP = gain
Profit = gain .....(1)

(as per the question when SP is doubled Profit is tripled )
Let increased SP = 2SP
INCREASED PROFIT = 3PROFIT
3PROFIT = 2SP - CP
3PROFIT = SP + SP - CP
From equation (1)
3profit = SP + gain ---> 2.
(1)/(2)

1/3 = gain/(gain + SP ) by inspection .
1/(1 + 2) = gain/(gain + sp).
Hence gain = 1.
SP = 2, hence CP = 1.

Using the formula
profit % = (gain/CP) * 100.
Profit % = 100.

Profit= SP - CP
Has per given in the question profit triples when SP doubles, hence alter the above equation accordingly
so, 3*Profit = 2SP - CP
3*(SP - CP)=2SP - CP -> since profit=sp-cp
3SP - 3CP= 2SP - CP
SP=2CP ->(1)


profit percent = (SP - CP)/CP*100 now sub (1) in this formula

=(2CP - CP)/ CP *100
=CP/CP * 100
=1*100=100%

You must read to know easy.
Here we note two points.

1. If we buy the things in " x " and selling in " y " the profit " p = y - x " .............(1).

2. If we buy the things in " x " and selling in " 2y " the profit triples (3p), So,

Profit = S.P - C.P.
3p = 2y - x ..............(2).

(1) implies (2),

3 (y - x) = 2y - x.
So, y = 2x.

Let c.p. be x and s.p. be y.

We know that;
profit =s.p.-c.p.
=y-x------------> equation 1.

According to question;

Selling price is doubled then the profit triples so,

3(y-x)=2y-x -------------> (selling price is doubled and profit is tripled from equation 1)
or, 3y-3x=2y-x.
or, y=2x.

Now, keeping the value of y in equation 1 we get;
profit =2x-x.
=x,
Profit%= profit/c.p.
= x/x*100%,
=100%.

Here, we have to make L.H.S = R.H.S for making equation (profit = profit).
Given S.P double thn Profit triple,
So, as considered C.P as X and S.P as Y,
S.P doubles then it is 2Y, But profit means S.P - C.P so it becomes 2Y-X, ---------- PROFIT (R.H.S)
Next given profit triples so profit means S.P - C.P, that is Y-X becomes 3(Y-X) --------PROFIT (L.H.S).

Equating R.H.S with L.H.S becomes 2Y-X = 3(Y-X).
Next, solve the equation.

Its just this that you can compare only similar things. Like profit with profit.

So, in this case when profit is thrice so SP is doubled.

So when it is equated.

3(y - x) = (2y - x)y = 2x.

In this profit as we know is (y-x) which is thrice.

So when we equate this we equate it with the profit at this time when it is thrice ok.

So the profit at this time would be SP-CP but here SP is twice at q so that is why 2y-x is there.

Let C. P is x answer S. P is y and initial profit is 10.

We know that S. P - C. P = Profit.

y - x = 10-> Eq 1.

According to given condition, if S. P Double profit become thrice of initial profit then, new S. P. Is 2y and profit is 30 and cost price is same as above x.

Now, 2y - x = 30 -> Eq 2.

By solving these two equation, we get x = 10 and y = 20.

So profit % = (y - x) /x= (20 - 10) /10 =100% this is a basic approach.

Very simple example..
Let,
c.p X= 2 and,
s.p Y1= 4.
Profit will be , P1=4 - 2= 2.

Now, check the condition if s.p is doubled, profit is tripled.
Means if Y2 = 2*Y1 ,
New profit will be P2= 3 * P1.

i.e, Y2 = 2 * 4 = 8,
And new profit P2 = 8-2 =6,
P2 = 3 * 2 = 6(condition satisfied).

Now check the % profit for original price.
%profit= [(Y1-X)/X]*100.
=[(4-2)/2]*100.
= [2/2]*100= 100%.

I don't think there should be necessary for explanation for this sum. It is just the common sense we need to apply. Coming to the Question.

If selling price is doubled, the profit triples. Find the profit percent.

I think we can answer this question without considering the 3 times of profit. I mean to read the question like this -- (If selling price is doubled, Find the profit percent.)

It is obviously 100%, right?