Aptitude - Profit and Loss - Discussion

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).

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.

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%

Alright I have another method here without assumption. First things first.

P=SP-CP. Since P=(320/100)CP Then (320/100)CP=SP-CP. SP=(420/100)CP

Next thing is getting the second equation. Our target is "what percentage of the selling price SP is the profit,P if we have a new cost price of (125/100)CP while SP remains the same?" So keep another P in mind which is x per cent of SP.

Therefore equation2 is xSP/100=SP-(125/100)CP

So xSP=100SP-125CP.

SP=(420/100)CP

xSP=100SP-125CP Eq2.

Substituting for SP in Eq2 then we have

x(420/100)CP=100(420/100)CP-125CP

xCP420/100=420CP-125CP. xCP420/100=295CP. x=295/4.2 x=70.23.

Note it has to be an approximated value according to the question which is 70.

Good explanation Malini!

@Mohana.

They have given profit%=320%. So to calculate profit we use the formula profit%= (profit*100) /C.P.

If you assume C.P=100 then always the profit% = profit for this simplicity we always assume C.P=100.

How they have taken the C.P value = 100
even it gives change to assume any number like 1,2,3, etc.,

25% cp is 1250 how that value get.

Why we are taking cp as 100?

In what cases we should assume in that way.

2. Why cannt we take that as x as in above sums.

Thanks Nitesh and malini for such a nice explanation.