Aptitude - Profit and Loss - Discussion

We know that.

P=S.P-C.P....(1).

Here the profit is 320% of the cost, so.

P= (320/100)*C.P....(2).

Substitute (2) in (1) instead of P.

We get (320/100)*C.P = S.P-C.P....(3).

From the equation (3) we can calculate the s. P in terms of C.P as.

S.P = (420/100)*C.P....(4).

Next we take the second condition: the cost is increased by 25%.

The new C.P is C.P+(25/100)*C.P....(5).

The equation (5) is substituted in the equation (1) instead of C.P.

We get P =S.P - (C.P+(25/100)*C.P).

P = S.P-C.P(1+(25/100))....(6).

We are calculating new profit (P) is how the percentage of the selling price (S.P).

Hence in equation (6) substitute C.P in terms of S.P.

We know the relation between s. P and c. P in equation (4) from that.

C.P = (100/420)*S.P....(7).

Substitute this c. P in to equation (6).

P=S.P-(100/420)*S.P*(1+(25/100)).

By solving we get : P = S.P (1-(125/420)) = 70% (approximately).

Let me explain,

1) Profit is 320% of Cost ==> Profit = (320/100)*CP.
Consider C.P is 100 then Profit = (320/100)*100 = 320.
Now Profit = SP-CP.
therefore, 320 = SP-100.
So, SP=420.

2) If the Cost increase by 25% ==> CP=100+25 = 125.

3)But the selling price remains constant ==> SP=420 (from 1st part).

Profit = SP-CP = 420-125 = 295.

4) What percentage of the selling price is the profit?
<<< for example, X% of Y is equal to (X/100)*Y >>>>
<<< 2% of 5 ==> (2/100)*5 >>>

From the above example, what percentage of the selling price is the profit==>

What percentage = ?
Of Selling Price = SP.
Is Profit = Profit.

(?/100)*SP = Profit.

Therefore, ? or Required percentage = (Profit * 100)/SP.

Required percentage = (295*100)/420 = 70%(approximately).

Alright I have another method here without assumption. First things first.

P=SP-CP. Since P=(320/100)CP Then (320/100)CP=SP-CP. SP=(420/100)CP

Next thing is getting the second equation. Our target is "what percentage of the selling price SP is the profit,P if we have a new cost price of (125/100)CP while SP remains the same?" So keep another P in mind which is x per cent of SP.

Therefore equation2 is xSP/100=SP-(125/100)CP

So xSP=100SP-125CP.

SP=(420/100)CP

xSP=100SP-125CP Eq2.

Substituting for SP in Eq2 then we have

x(420/100)CP=100(420/100)CP-125CP

xCP420/100=420CP-125CP. xCP420/100=295CP. x=295/4.2 x=70.23.

Note it has to be an approximated value according to the question which is 70.

Why don't we do like this:

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

If x% be selling percentage of profit then,

x*S.P = S.P-C.P.

S.P- (x*S.P) = C.P.

S.P (1-x) = C.P.

(S.P/C.P) = (1/1-x).

Now when we see the problem he given a clue that p = 320% (C.P).

S.P-C.P = (320/100) (C.P).

S.P-C.P = (3.2) C.P.

S.P = (3.2) C.P+C.P.

S.P = (4.2) C.P.

S.P/C.P = 4.2 =>A.

When C.P increases 25%, S.P is remains same then.

S.P/ (C.P+ (25%C.P) ) = (1/1-x).

S.P/ (1+0.25) C.P = (1/1-x).

S.P/ (1.25) C.P = (1/1-x).

(1/1.25) (S.P/C.P) = (1/1-x).

Substituting from A (S.P/C.P) = 4.2.

(1\1.25) (4.2) = (1/1-x).

(3.36) = (1/1-x).

(1-x) = (1/3.36).

1-x = (25/84).

x = 1- (25/84).

x = (59/84) = ~70% (approximately).

The point is in 'what context' the profit percentage is to be calculated?

Is it relative to cost price or selling price?

Well!, when you're asked to find the profit %, its relative to the 'selling price'.

That's why in the above problem the answer is 70%. If we consider the cost price as the base to find the profit %, then it would be 236%. But this is wrong.

To understand this more,

Draw a pie diagram, taking the selling price (420) as the full circle and mark the proper fractions for cost price (125) and for the profit (295). Just see the portion of profit and determine the area covered in the circle, that's the profit %.

Let me explain you clearly:

In most of the problems assume cp as 100 then only it will be easy.
now let us assume cp=100
profit is given 320%
we know p=sp-cp
then sp=p+cp
so sp=420

Then it is given cp is incresed by 25%
so cp=alredy assumed as 100+now increased by 25%
cp=125
sp is always constant(given in question)
so now sp=420
cp=125
p=sp-cp
=420-125
=295
p%=p/cp*100

But here it is specifically asked for sp(read the question)
so p%=p/sp*100
=295/420*100
=70%

Let, Cp = x & Sp = y.

According to question,

The profit is 320% of the cost,

Gain = (320/100)*x = 3.2x.
Gain = Sp-Cp.
3.2x = y-x.

x = y/4.2....(1).

If the cost increases by 25% but the selling price remains constant.

Cp = (x+x*25%).
= (x+ 0.25x).
= 1.25x.

Sp = y (because of constant).

Then, Gain = y-1.25x.

By equation (1) put the value of x in above equation.

Gain = y-1.25*(y/4.2).
Gain = y*(.70).
= 70% of y.

Thank you.

@Nitesh.

Your answer is wrong.

25% of 1000 is 1250(right).
& 320% of 1000 is 1320(how?).

32% of 1000 is 1320.
320% of 1000 is 3200.

So,
Let C.P = 1000.
profit = 320%.

But profit = S.P - C.P;
than S.P = 1000+3200.
= 4200.

Now given that C.P is increased by 25 %.
Then C.P becomes 1250 and S.P is constant.
Hence,

= (4200-1250)/4200*100.

= 70.23.

But if you make C.P is 100 than it will be easy.

Let CP =100 rs.

From ques. SP = 320% of CP = 100+320 =420 rs.
Now ques says that CP is increased by 25% .it means now CP = 125 rs
But, SP remains constant.
Now Profit = 420 - 125=295 rs

From the question, we have to find out the PROFIT % at SP(420 rs.)
So P% = (295/420)*100 = 70%.
(SP-CP)/CP is not a formula actually. this is only for our comfort to find out an easier way to solve problems.

Given:
profit=320%.
C.P = increases 25%.
S.P = remains constant.
Asking, S.P % if C.P is increased 25% for the profit 320%?
Generally, when C.P. increases 25% obviously S.P decrease 25% for the same 320%profit.
i.e, S.P - C.P = Profit.

If, S.P(100) - C.P(100) = 320.
Then, C.P(125) - S.P(75) = 320 [when C.P increases 25%],
Therefore, S.P = 75%,
Approximately, S.P = 70%.