Aptitude - Profit and Loss - Discussion

Profit = 22.5.
S.p = 392. I want cost price=?
Let c.p = 100 . Because we find out percentage as 100 Every where. C.p/100 = S.p/122.5.
C.p/100 = 392/122.5.
C.p = 320.
Profit = s.p - c.p = 392 - 320 = 72.

In this question we have to find profit value,

We all know that profit =SP - CP.

Here s. P=Rs.392(which is given in the question)
Now we have to find c. P value then only we will get the profit value
By using this formula C. P=100/100+gain %*s.p(given in important formulas)
Then c. P=100/100+22.5*392(here gain% and s. P values are given in the question)
C.p=100/122.5*392

By simplifying this we will get CP value,
Therefore c. P=Rs. 320,
Now substitute the SP and CP values in profit formula.
Profit = SP- CP.
Profit =Rs. (392-320),
Profit =Rs. 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).

As in the question SP= 392 Rs.
And Profit% the shopkeeper gets = 22.5%,
The CP is not given so let's take it as x.

we know that Profit% = Profit/CP * 100 (Profit= SP - CP).
Therefore 22.5 = 392-x/x * 100.
By solving we get 22.5x = 39200 - 100x,
x = 39200/122.5,
x = 320 which is CP.

So the conclusion is Profit = SP - CP.
That is 392 - 320 = 72.

Let C.P. be 100,

Profit gave 22.5
According to it S.P. It Will be 122.5,

If we take the ratio of S.P. and C.P. it will be 122.5/100.
But according to question S.P given is 392 and we will let C.P. be x.
now 122.5/100 = 392/x.
it will be x = 320.
So, CP is 320 and S.P. is 392,
Profit = S.P - C.P.
= 392 - 320.
= 72 is our profit.

Profit=22.5%. and SP=392
Then CP * 122.5/100 = 392.
After solve we get CP = 320,
Now simple (sp-cp) = 72.

I think it will help you.
Thanks have a great day.

(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.

Short Trick to Solve this Question is likewise.

We know Selling Prize is 392 & Profit Percentage 22.5 %.
So,

CP = SP * P/100.

= 392 * 1225/1000.
= 320.

So, Profit = SP - CP.

P = 392 - 320 = 72.

Note: (If SP & Profit/loss % is given then Cp = SP * 100/P/l%. But, if CP & Profit/loss % is given then Sp = CP * P/L%/100).

@Ragav.

Basic formula is cost + profit = selling price.

Here we assume cost is 100. given profit is 22.5%.
CP + P= SP Which means 100 + 22.5 = 122.5.
So, we get SP 122.5 which is 392.
122.5 = 392
22.5 = x

Just cross multiply it you'll get the answer.

Profit%= s.p - c.p/ c.p.

Let x be the cost price.
Here profit %= 22.5.
S.p = 392 is given.
According to formula.
22.5/100= 392.

22.5x = 39200 - 100x.
122.5x = 39200.
X = 39200/122.5.
X = 320.
So, c.p is Rs 320.

Now finding profit.
Profit = s.p - c.p.
Profit = 392 - 320.
Profit = 72.