Aptitude - Profit and Loss - Discussion

How we will get the value 420?

Let me explain,

1) Profit is 320% of Cost ==> Profit = (320/100)*CP.
Consider C.P is 100 then Profit = (320/100)*100 = 320.
Now Profit = SP-CP.
therefore, 320 = SP-100.
So, SP=420.

2) If the Cost increase by 25% ==> CP=100+25 = 125.

3)But the selling price remains constant ==> SP=420 (from 1st part).

Profit = SP-CP = 420-125 = 295.

4) What percentage of the selling price is the profit?
<<< for example, X% of Y is equal to (X/100)*Y >>>>
<<< 2% of 5 ==> (2/100)*5 >>>

From the above example, what percentage of the selling price is the profit==>

What percentage = ?
Of Selling Price = SP.
Is Profit = Profit.

(?/100)*SP = Profit.

Therefore, ? or Required percentage = (Profit * 100)/SP.

Required percentage = (295*100)/420 = 70%(approximately).

If we take cost prize 1000, then profit will not be 320, cause in question profit is 320 percent of 1000, which is not equal to 320.

We are all know that gain% in terms of C.P price but in the given problem gain% in terms of S.P.

I have one doubt if the question is asked like what's the percentage of the selling price is the profit means we have to use denominator as s.p ah?

I have a doubt here in question's 2nd part here we know that %profit calculated by CP but here?

Please give shortcut for this.

@Nitesh.

If I take CP = 100 I'm getting wrong answer can please help me?

Let, Cp = x & Sp = y.

According to question,

The profit is 320% of the cost,

Gain = (320/100)*x = 3.2x.
Gain = Sp-Cp.
3.2x = y-x.

x = y/4.2....(1).

If the cost increases by 25% but the selling price remains constant.

Cp = (x+x*25%).
= (x+ 0.25x).
= 1.25x.

Sp = y (because of constant).

Then, Gain = y-1.25x.

By equation (1) put the value of x in above equation.

Gain = y-1.25*(y/4.2).
Gain = y*(.70).
= 70% of y.

Thank you.

New C.P. = 125% of Rs. 100 = Rs. 125.

New S.P. = Rs. 420.

Profit = Rs. (420-125) = Rs. 295.

Required percentage = 295x 100% = 1475% = 70% (approximately).

This step 1 didn't get.