Aptitude - Profit and Loss - Discussion

In the question, Actually we want to find the profit %, if an article was sold by giving 5% discount on the list price.

List price is differ from cost price.

For Eg: If a mobile store bought a mobile for 5000rs from manufacturer company, but MRP printed on the mobile would be 7000Rs. They will sold the mobile by giving 5% discount on the MRP.

So MRP--> list price.

Sol:

Assume List price = MRP = Rs X.

if he sold by giving discount 5%,
then S.P = (100-5)% of X.
= 95% X.
S.P = 19/20 X.

So if he sell an article for rs (19/20)X, what would be the profit he gained? is the question.

To find the profit, we need Cost price of the article.

Here we can't take the CP from the 3rd sentence as Rs. 5000, because from this we cant able to find the profit.

Profit = (19/20)X-5000 = unpredictable.

So we want to go with the 2nd sentence.

If in a case, if the seller sell the article without giving any discount on the list price(MRP) and he will get 20% gain more than the cost price.

Then S.P = MRP = Rs X.

Since he got 20% gain more than the cost price.

S.P = 1.2 C.P.

=> C.P = Rs (5/6)S.P = Rs (5/6)X.

Which gives the actual cost price of the article.

Profit = S.P - C.P.
= (19/20)X - (5/6)X.
= (7/60)X.

Gain % = (Profit/C.P)*100.
= 14% (by solving).

So 1st and 2nd sentences gives us the answer.

We can't take 2 and 3, because it gives the same profit % as 20% which is not our answer.

And even though we want calculate the profit % by taking the 1st sentence because that is the question.

I want to say that if we take 2nd statement only.

Let the selling price be x.
Gain percentage =20% (given in 2nd statment).
Gain percentage= ( (sp-cp) /cp) *100.
Therefore 20= ( (x-cp) /cp) *100.
Which gives cp= (5/6) *x.
Profit percentage = ( (sp-cp) /cp) *100.
Profit percentage= ( (x- (5/6) x) / (5/6) x) *100.
Profit percentage=20% approximately.

Am I right? Correct me If I am wrong.

After giving 5% discount on list price,
sp=x-5*x/100=19x/20.

In 2nd case no discount is given that means marked price = sp.
So sp = x.

Again to gain 20% cp should be,
cp = 100*x/(100+20) = 0.833x.

Now to find profit take sp of when this is given so,

Profit = (sp-cp)*100/cp = (0.95-0.833) *100/0.833 = 14%.

So statement 1 and 2 are only needed to answer.

List price and cost price are two different terms.

List price is we can say what is written on the product whereas cost price is at what price it is given to the customer. So don't get confused with both the terms. This will make you understand the question easily.

But why not third statement is true like.

cp = (100/100*gain%)*sp from third statement.

Where we know,

sp = 120% of cp from statement 2nd.

So we can say,

cp = (100/100+gain%)*120% of cp which 100 + gain% = 120.

Gain% = 20.

Here we assuming initial gain of 100% and then we are taking increased gain of 120%. But if we will take any unknown gain of R%, then all statement must required.

Why II & III couldn't be the answer?

C.P=5000;then if 20% profit is gained the profit amount will be = 1000,
Then by the formula, Gain%=(Gain*100)/C.P.

I think we can also come to a solution using II and III;
CP = 5000.
SP = 120%(CP) = 6000.
Thus profit = 1000 and profit% = 20%.

In given explanation,

I-> x is list price
II-> x is selling price

So how did you equte them?

@Prasu :-

Cost Price = [ (100)/(100+gain%)]* Selling price

= [100/120]x