Aptitude - Profit and Loss - Discussion

Suppose, CP = 100,
Profit = x,
Selling Price = 100 + x.

=>According to question,
2 * SP = CP + (3 * Profit).
Or, 2(100+x) = 100 + 3x.
Or, 200+2x = 100 + 3x.
Or, 3x - 2x = 200 - 100,
Or, x =100.
=> Profit = 100%.

Here, we have to make L.H.S = R.H.S for making equation (profit = profit).
Given S.P double thn Profit triple,
So, as considered C.P as X and S.P as Y,
S.P doubles then it is 2Y, But profit means S.P - C.P so it becomes 2Y-X, ---------- PROFIT (R.H.S)
Next given profit triples so profit means S.P - C.P, that is Y-X becomes 3(Y-X) --------PROFIT (L.H.S).

Equating R.H.S with L.H.S becomes 2Y-X = 3(Y-X).
Next, solve the equation.

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

So the profit is (y - x) ---------------------------- (1)

Now, the S.P. is doubled. So the new S.P. = 2y.
The new profit = (2y - x).

Given that when S.P. is doubled, profit increases 3 times
=> New profit = 3 * old profit,
=> (2y - x) = 3(y - x),
=> y = 2x.

So, the profit = (y - x) = (2x - x) = x.

% profit = (x * 100)% = 100%.

P= sp -cp.
2x -x = x.
P% = x/x * 100%,
100%.

The value of sp = 2x bcoz SP was doubled then cp=3x (cp was tripled).
pf = sp - cp

So the solution is:

pf = 2x - 3x = pf/100%.
=x = 1x/100%,
then x = 1/100,
Ans:100%.

Since c.p. remain unchanged .let it be Rs. x.
Let s.p. = Rs y.
Profit= y-x.

If s.p. is doubled i.e it becomes 2y then profit = 2y -x.
As given that this profit is trippled.
i.e. 3*(y-x) = 2y-x.
From which we get (y/x)=2.
%profit = (profit/c.p) * 100.
= (s.p./c.p.-1) * 100,
= (y/x-1) * 100,
= (2-1) * 100,
= 100% Ans.

Why 2y-x? Explain it.

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.

A table is sold at a profit of 20%. If the cost price and selling price are rs200 less, the profit would be 8%more, find the cost price.

Can anyone solve this?

Good explanation @Raj.