Aptitude - Profit and Loss - Discussion

Just assume cost of price is 100 then profit is 320 so total cost of product is 320+100=420 if cost increases 25% i.e 125 then profit decreases 420-125=295(profit) 295/420*100=70%

Lets assume cost to be 10.

profit = 320/100*10
=32.

S.P = CP + P
=10+32
=42.


Now cost increased by 25% (25/100*10=2.5)
=10 + 2.5
=12.5.

SP remaining the same 42

SP=C + p
42 =12.5 + x
29.5 = x.

So,
If 42 is 100, how much would be 29.5?
Cross multiply

42=100.
29.5=?

Ans: 70.

Why don't we do like this:

We know that p = S.P-C.P.

If x% be selling percentage of profit then,

x*S.P = S.P-C.P.

S.P- (x*S.P) = C.P.

S.P (1-x) = C.P.

(S.P/C.P) = (1/1-x).

Now when we see the problem he given a clue that p = 320% (C.P).

S.P-C.P = (320/100) (C.P).

S.P-C.P = (3.2) C.P.

S.P = (3.2) C.P+C.P.

S.P = (4.2) C.P.

S.P/C.P = 4.2 =>A.

When C.P increases 25%, S.P is remains same then.

S.P/ (C.P+ (25%C.P) ) = (1/1-x).

S.P/ (1+0.25) C.P = (1/1-x).

S.P/ (1.25) C.P = (1/1-x).

(1/1.25) (S.P/C.P) = (1/1-x).

Substituting from A (S.P/C.P) = 4.2.

(1\1.25) (4.2) = (1/1-x).

(3.36) = (1/1-x).

(1-x) = (1/3.36).

1-x = (25/84).

x = 1- (25/84).

x = (59/84) = ~70% (approximately).

So the conclusion is that we can assume any value for cp if not mentioned?

Here, profit % is calculated on SP i.e. 420.

But, it should be calculated on CP i.e. 100.

There is some confusion for profit% formula. Please give me answer ?

If question asking to Profit % on SP then Formula should be used -
Gain % = profit*100/SP.

If question asking to Profit % on CP then Formula should be used -
Gain % = profit*100/CP.

@Nitesh.

Your answer is wrong.

25% of 1000 is 1250(right).
& 320% of 1000 is 1320(how?).

32% of 1000 is 1320.
320% of 1000 is 3200.

So,
Let C.P = 1000.
profit = 320%.

But profit = S.P - C.P;
than S.P = 1000+3200.
= 4200.

Now given that C.P is increased by 25 %.
Then C.P becomes 1250 and S.P is constant.
Hence,

= (4200-1250)/4200*100.

= 70.23.

But if you make C.P is 100 than it will be easy.

I understood everything but. Why you have taken S.P instead of C.P in the formula of profit percentage. And if its a theorem or formula so exactly where-2 we need to use this method.

@Payal.

Question itself is asking 'What percentage of selling price is the profit'.