Aptitude - Profit and Loss - Discussion

Lets cost price of each article be 4.
So cost price of 20 articles = 20*4=80.
So selling price of each article = 4+4*25%= 5.

So selling price of x articles = 5x.
So according to the question 5x = 80.
So x = 80/5= 16.

Simple it is.

S.P for x articles = C.P (of 20 articles).
Then S.P for 20 articles = ?

S.P = (20/x) *C.P---------- 1.

Profit%= (profit/C.P) *100.
(25/100)*C.P = profit, so profit=C.P/4----------- 2.

But actually formula.
S.P - C.P = profit.

From 1 & 2.

(20/x) *C.P - C.P = C.P/4.

20/x = 5/4.

X= (20/5) *4=16.

I think you understand this simple way of thinking.

Just logic:

In question : profit% has given so S.P>C.P.

So if S.P for xnos is equal to C.P for 20nos.

So S.P for 20nos should be more than S.P for x nos then we will get profit.

So simply S.P for 20 nos > S.P for x nos.

We know already S.P for x nos = C.P.

Then you can find S.P for 20 nos.

That's it.

I wanted to ask why do we take the C.P of x articles? in the Question it is stated that the C.P of 20 articles so we should find the C.P of 20 instead, no?

Let 20 article price = 20 RS.

.'. Selling price of x article = 20.
25% profit(means cost is 100 then sp 125).

If SP 125 then CP 100.
...... 20 ..... (100/125)*20 = 16.

SP = 20.
Gain = 25%.
CP = ?

CP = (100*20)/(100+25).

Let cost price of an article be "a"
Let selling price of an article be "b"

Cost price of 20 articles is the same as the selling price of x articles. i.e;
20*a = x*b.

Profit = 25%.
((total articles * b) - (total articles * a))/(total articles * a) = 25 /100.

=> (20b-20a)/20a = 1/4.
=> b=5a/4.

Substitute b in 1st equation,
x=16.

It is very simple.

It is given CP of some number of articles is equal to the SP of other number of articles.

Something like this,

CP of 20 apples = SP of 15 apples.

20*CP of each apple= 15*SP of each apple.

20*CP = 15*SP.

NOW just put the formula.
Gain% = CP-SP/CP*100.

Can you explain me about the assumptions it makes me difficult to understand?

Now, This is simplest way I could relate:

No. of articles = 20.
Let CP of 1 article = Re. 1.
CP of 20 articles = Rs. 20 ..... (Eq. 1).

SP of 1 article = 1.25x1 = Rs. 1.25 (Since profit is 25%).
SP of X articles = 1.25X .... (Eq. 2).

Now, the statement says the CP of 20 articles = SP of "X" articles with a profit of 25% i.e. Eq. 1 = Eq. 2.

20 = 1.25X.
X= 20/1.25 = 16.

Hope it clears !.

Let SP of 1 article = RS 1.
Then SP of X articles = RS X.

ACCORDING TO GIVEN,
CP of 20 articles = SP of X articles.
CP of 20 articles = RS X.
CP of 1 article = RS X/20.

SP = CP ( 1 + R/100 ).
1 = 125/100 * X/20.
X = 16. ans (this is the most simplest way).