Aptitude - Profit and Loss - Discussion

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

Here Take it as Ratio method.

Consider to 3:2.

Her Profit = 3.
Selling Price = 2.

3-2 = 1.
1 * 100 = 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%.

PROFIT (P) = Selling Price(S) - Cost Price(C).

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

As per the question.

3P = 2S-C.

3(S -C ) = 2S- C -------> from EQ 1.

S = 2C --------> by Simplifying.

Now P%= ((S-C)/C ) *100.

= ((2C-C)/C)*100 = 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%.

We know that SP/CP=(100+G%)/100.

So as per given question.

SP1/SP2=(100+G1%)/(100+G2%).

==> SP/2SP=(100+G)/(100+3G).

==>1/2=(100+G)/(100+3G).

==>G=100.
So
Profit=100%.

Let the C.P be x and S.P be y.

Profit = S.P-C.P = y-x given question if the S.P doubles then profit will triples therefore,

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

y = 2x.

Profit = x.

Profit% = x*100/x = 100.

Profit is 100 percent.

Formula's used:

1) Profit = SP-CP.

2) Profit % = Profit/CP *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%.

When selling price doubled even cost price is also doubled than how this comes SP = 2y-x ?

CP = x,
SP = 2x,

Profit = SP - CP.
= 2x-x.

Profit = x.

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

= (x/x)*100.

=100%.