Aptitude - Profit and Loss - Discussion

PROFIT = S.P - C.P.

Shopkeeper expects a gain of 22.5% on his cost price.

i.e S.P = C.P + 22.5% of C.P.

= C.P(1+(22.5/100)).

S.P = 1.225 C.P.

His sale was of Rs. 392 i.e S.P = 392.

392 = 1.225 C.P.

C.P = 320.

(S.P. - C.P.)/C.P. = gain(Over here it is 22.5)/100.

Which is same as,

S.P./C.P. - 1 = gain / 100 //JUST DIVIDE BY DENOMINATOR AT L.H.S

S.P. / C.P. = 1 +(gain / 100) //TAKE 1 ON R.H.S

S.P./ C.P. = (gain + 100) / 100 // SIMPLIFY R.H.S

C.P. = 100 * S.P. /(gain + 100)

This formula has come from the basic concept of profit.

Let C.P is X.

And S.P is 392.

By formula, gain % = (gain*100)/C.P.

Here gain = 392 - X.

So,

22.5 = {(392-X)100}/X.

122.5X = 39200.

X = 320

So C.P = 320.

Profit = 392 - 320.

= 72.

We consider CP as 100%.If he got a profit of 22.5%, we can say that SP is 122.5% of CP.
If this 122.5% of CP=392(given in question).
Then 100% of CP=320 (this can be done through cross multiplication).

Through difference B/W SP and CP we can get the profit as Rs.72.

OR

Here given that CP+profit=392.
CP is considered 100% and he made a profit of 22.5% on this CP,
Then SP=122.5% of CP=392,
Then 22.5% =72(through cross multiplication).

Thanks preitee nice explanation.

From the question, where from you take 122.5%.

Normally take 100%. if 22.5% increase means 122.5%.

122.5% =392.

So 1% =392/122.5=3.2.

So 100% =100*3.2 =320.

Profit =392-320.

Answer: 72.

Thanks Mrs Pallavi

SOLUTION FOR C.E.=(100/(PROFIT%)*S.E.)