Aptitude - Profit and Loss - Discussion

First of all, in the problem they had given that if selling price doubles, profit will be tribled.

Actually we have the formulae that,

Profit = selling price - cost price.

Let the selling price be y and cost price be x.

From formulae above profit= s.p - c.p.

Profit= y - x -----> (1).

From the data given, if selling price doubles, profit will be tripled. so that,

From(1), we can write

Profit = y-x, here from the data given if y doubles profit will be tripled. so we can write in place of profit we can write y-x.

3(y-x) = 2y-x,
y = 2x,
profit from (1),
profit = 2x-x.
= x.

Then we have to calculate profit percentage, so we have formulae for profit percentage
Profit%= (profit/cost price) * 100,
= (x/x) * 100.

Profit% = 100%.
Thus the answer is crystal clear.

I am explaining the question in accordance with CP=x and SP=y.

The real confusion in this question is that in the statement they have said "selling price is doubled", which means the equation should be 2y = 3(y-x).

But this is wrong, because on left side we are taking only NEW SP but the right side the equation is in terms of Profit.
Remember they have given the relation if SP and Profit in proportionality and NOT EQUAL.

But, we have to make an equation in terms of profit on both sides. So, to get the new Profit, the SP is doubled and the original CP is subtracted from the same i.e. 2y and then subtract the CP from it which gives the equation as : (2y-x) .

I hope the rest is clear to all .. the same is very well explained by @atul

Thank you.

Let cost price = x and selling price = y.

Then, in question they saying that the selling price is double a and profit triple that means.

First condition here our selling price is y then according to question will be 2y.

Second condition and again they are saying that our profit is triple and our profit is x-y i.e. cp-sp = profit.

Then according to question here our profit = 3(y-x).

Then according to first condition we will get:

Profit = (2y-x) ----- (1).

And according to second condition will get:

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

By using equation (1) and equation (2) we will get:

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

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

After solving this equation we will get 100% profit.

Thanks friends and good luck. And according to second condition we will get.

Observe that there are two cases given in this question.

We know that for solving two variables we need at least two relations.

Here,
Case 1.
CP is x.
SP is y.
So, the gain is y-x.

Case 2.
CP is x
SP is 2y (sp is doubled)
So, the gain is 2y-x (according to question this quantity is 3 times the gain in Case 1).

On solving case 1 and 2 according to the question.
3(y-x)=2y-x.
Or y=2x.

Now, it is observable that they are asking the gain% of case 1 (case 2 is only given for finding a relation between x and y).

So the gain per cent (of case 1) will be;
Gain% = (gain/cp)*100.
= {(y-x)/x}*100,
= {(2x-x)/x}*100.

Gain% = (x/x)*100.
Gain% = 100%.

I hope you notice that the question asks for gain% for case 1.

Thank you

Some people are confused by this question because they are confused to calculate profit after doubling selling price or before doubling selling price. Many people had given about general logic. Now it tell in short cut manner by taking value.

Consider C.P = 100, S.P = 200 then double S.P = 400.

Earlier profit is 100 and after doubling we get 300 which is tripled of profit earlier.

Now they asked us to find profit % question is not clear about finding profit but options makes it clear about finding the answer i.e. if you see earlier profit % it is 100% but after doubling selling price it is 300%.

So by seeing options we can say that 100% is the correct answer since 300% is not given. This type of questions will be cleared by options.

First of all, in the problem, they had given that if selling price doubles, profit will be tripled.

Actually, we have the formulae that profit = selling price - cost price

Let the selling price be y and cost price be x.

From formulae above profit= s.p.-c.p.

Profit= y-x___________(1)

From the data given, if selling price doubles, profit will be tripled. so that
From(1), we can write

Profit=y-x, here from the data given if y doubles profit will be tribled. so we can write in place of profit we can write y-x.

3(y-x) = 2y-x.
y = 2x.
profit from (1)
profit =2x-x,
= x.

Then we have to calculate profit percentage, so we have formulae for profit percentage
Profit%= (profit/cost price)*100.
= (x/x)*100.
Profit% =100%.

First of all, in the problem they had given that if selling price doubles, profit will be tribled.

Actually we have the formulae that
profit = selling price - cost price

Let the selling price be y and cost price be x

From formulae above profit= s.p.-c.p.

Profit= y-x___________(1)

From the data given, if selling price doubles, profit will be tribled. so that

From(1), we can write

profit=y-x, here from the data given if y doubles profit will be tribled. so we can write in place of profit we can write y-x

3(y-x) = 2y-x
y=2x
profit from (1)
profit=2x-x
= x

Then we have to calcute profit percentage, so we have formulae for profit percentage
Profit%= (profit/cost price)*100
= (x/x)*100

Profit% =100%.

Don't take x, y. Simply assume let COST PRICE = C.P,SELLING PRICE = S.P.

STEP-1:

According to question profit tripled,
i.e 3*PROFIT, and we can write profit = S.P - C.P.
So it becomes, 3*(S.P-C.P) --- equation 1.

STEP-2:

Also its given S.P is doubled i.e 2*S.P.
According to us profit should be,
Profit = S.P - C.P (Formula)
= 2*S.P - C.P ---- equation 2.

STEP-3:

Compare both equations because both shows profit,
3*(S.P-C.P) = 2*S.P-C.P.
3S.P-3C.P = 2S.P-C.P.

Now taking S.P one side and C.P another,
3S.P-2S.P = 3C.P-C.P.
S.P = 2C.P.

STEP-4:

Profit = S.P - C.P (formula).
= 2C.P - C.P.
Profit = C.P.

Using above in formula now,

Profit% = profit/cp*100.
= C.P/C.P*100.
= 100%.

Most of you get confused by this question because you think that we have to find the profit percentage when the selling price is doubled.

But it's not like that.

They have just given a clue to assume how to take profit.

Let's take C. P as x and S. P as why;
We know that profit is S. P - C. P.
Twice the selling price is not equal to thrice the profit.

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

Here, when selling price is doubled (2y) , at that time the profit i.e., (2y - x) is equal to thrice normal profit value3 (y - x).

Then simplifying this 2y - x = 3 (y - x), you will get y = 2x.
Hope you will do the remaining.

Lets say, c.p.= x and,
s.p.= y initially.
according to formula,
s.p. - c.p. = profit,

So, (y-x) = profit at initial. ....[1]
Now, s.p. is doubled, it becomes 2y
The profit is tripled, it becomes 3(y-x).
But c.p. remains same, it is x.
Again using formula,
s.p. - c.p. = profit.
2y - x = 3(y-x).
3x-x = 3y-2y
2x = y (s.p.)

The question have asked how much profit percent after condition applied
So, we have to consider initial c.p. (x) and final s.p. (2x) (from above solution)
Profit= s.p. - c. p.
= 2x - x
= x.

Profit % = (profit/c.p.)*100
=x/x *100
=100%.