Aptitude - Profit and Loss - Discussion

I believe your all wrong. There are too many assumptions in this problem.

Nothing is mentioned about the cost. Every single one of you are doubling the cost to get the selling price. The question specifically says double the selling price, not double the cost. If you make a table, this is a better visual.

-------> initial ----- new
SP---> 10 ----- 20
CP---> -5 ----- (- 5)
P---> 5 ----- 15

Selling price as you can see is double and profit is tripled. Cost does not change. Profit is tripled.

Hi, even if the selling price is doubled, we have to consider the cost price also to find the profit. What you mentioned was correct but not all the problems.

See if the sp is 100 and if it is doubled then sp =200, bot the cost price may be 50.. so the profit is 150 not 100.. so here the profit is 150%. so we have to consider the terms 'the profit triples.

Say sp = x
profit = y
then
x-cp=y(general eqn sp-cp=gain)
2x-cp=3y(condition given in the problem)

solving these two we get

y=cp

so the profit is 100%

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

Up to this equation, it is fine.

But next when we calculate profit. we are using profit = y-x.

Here we take the older value of our selling price that is y.

But why don't we take the new value of our selling price that is 2y.

Like suppose originally our cp = 100, sp = 200, profit = 100.

Now cp = 100, sp = 400, profit = 300.

( that is sp double, profit triple)

So now, profit % is (sp-cp)/cp*100.

=(400-100)/100*100.

=300%.

Is it now correct or ans is 100%.

Friends,

We know p(profit)= s.p - c.p,

let s.p = y, c.p = x, hence p = y - x (profit = s.p - c.p)--------> (1)

Now according to question when sp gets doubled ie (2y) profit triples so, the formula p = s.p - c.p now becomes 3*p = 2*y - x.

Next step is substituting p = y - x in above equation we get,

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

Now substitute the value of y in eqn (1),

p = y-x.
p = 2x-x.
p = x.

Now Profit%=(profit/cp)*100.

i.e. Profit% =(x/x) * 100.

Profit% = 1*100.

or 100%.

For all who don't understand.

Let,

A = Cost price.

B = Selling price.

C = b - a = Profit.

When selling price is doubled;

Cost price = a.

Selling price = 2b.

Profit = 2b-a --------> (1).

Given that when selling price is doubled, the profit triples;

Ie profit = (b - a) x 3 = 3b - 3a --------> (2).

Equation (1) and (2) are equal, on equating;

3b - 3a = 2b - a ie b = 2a.

B = 2a means the selling price is twice as that of the cost price, which means the profit is another 'a'. (ie) 100%.

We know,

p%= ( sp - cp ) / cp * 100-----(1)
So we have sp - cp = ( p *cp )/100-------(2)
we are given that profit is tripled and sp is doubled

So we have profit % 3p.
from one replace p by 3p and sp by 2 sp
we arrive at,
3p=(2sp - cp)/cp *100.
so now
(3p*cp )/100 =2sp - cp.
3(p *cp)/100 =2sp -cp.
we can replace p*cp/100 with (sp-cp) -----from (2).
so 3(sp-cp)=2sp - cp.
3sp-3cp=2sp-cp.
sp=2cp -(3).
so now we have from 1.
p%=2cp-cp/cp *100 (replace sp=2cp).
p%=100.

This solution is;

Because in the question profit or gain is being mentioned.

So G(Gain) = Sp(selling price) - Cp(cost price) ------> (1)
Or eq.(1) can also be written as;
Sp = (G+Cp) ------> (2).

And by what the question says we can make an equation as follows;
3G = 2Sp - Cp ------> (3)

Eq(2) in eq(3) and after solving eq(3).
We get G=Cp ------> (4).

Now in Gain% formula.
G% = (G*100)/Cp ------> (5).
Put the value of eq(4) in (5).
And G% equals to 100 (The answer).

Really I am confusing about this question. Because Q)If selling price is doubled, the profit triples. Find the profit percent.

SP double means we always determined SP on CP. So obviously CP = x and SP = 2x.
And profit always depend upon diff btw SP and CP. So Profit = x.

But according to question profit = 3X.

Then profit% = (profit/CP)*100.

If profit = X then P%= 100%.

But as per question p=3X so profit = (3x/x)*100 = 300%.

How is it possible. Please clarify my doubt?

Let say C.P = X,
Then, S.P = Y, (Consider Y value is double the X, so can write as Y=2X).

As per the question profit = 3X,(you can just use this value for validation).

So the profit = S.P - C.P = Y-X.

Profit percentage = Y-X / X * 100.
= 2X-X / X * 100 = 100% .

(here the Y value has been substituted)

Now, you can validate the answer.

3X =100
So X = 100/3
= 33.3 ( X= C.P = 33.3 ).

Y(S.P) = 2X = 2 * 33.3
= 66.6 (double the C.P).

I think the simplest solution is this.

As we know (Profit %) = (S.P - C.P) * 100 / C.P ---> EQUATION 1

In question say S.P is doubled & Profit is Tripled(not Profit %)

So Assume C.P= C S.P= S Profit = P.

As we know Profit = S.P - C.P.
So P = S - C ---> Eqn.1
As given Sale price is doubled & Profit is Tripled
So 3P=2S-C ---> Eqn.2

By solving this both Eqn. we get S=2C Means SP=2CP.

Put this value in starting Equation 1 you'll get 100% as answer.