Aptitude - Profit and Loss - Discussion

Let's say C.P of one article be "k" and S.P of one article be "y".

So, C.P of 20 article is "20k" and S.P of x article is "xy'

According to the question we know,
C.P of 20 article = S.P of x article.
Therefore, 20k = xy ------------> (1)

Also for a profit of 25% we can write equation as,
=> S.P of one article - C.P of one article / C.P of one article X 100 = 25
=> y - k / k = 1/4
=> 4y = 5k ------------> (2)

From equation (1) and (2) we can say that,
=> 16y - xy = 0,
=> y(16-x) = 0,
=> x = 16 [ANS].

cp = xsp.
20 = 125%x
20 = 5/4x
20 * 4/4 = x.
16 = x.

Let us assume c.p of one article = rs.1.
c.p of x articles = x,
s.p of x articles = c.p of 20 articles = 20,
profit = s.p-c.p = 20-x.
profit% = 25%.
profit% = (profit/c.p )* 100.
25 = (20-x/x )*100.
25x = 2000-100x.
2000 = 125x.
x=16.

Let the CP of 20 articles be 100.
If SP is 25% profit, then it would be 125.
If 20 articles are 100.
Then,
x article is 125.

Just simply multiply the values and equal it;
x * 125 = 20 * 100.
x = 16.

Given:
20cp = x sp.
20cp = 125% cp * x (because profit is 25 %).
20cp = 5/4 cp * x.
20 x 4/5 = x.
16 = cp.

cp = 100 - 20 = 80,
sp = 25/100 * 20 = 5,
80/5 = 16.

Let c.p(20) = s.p(x) = 100.
c.p(1) = 100/20 = 5
s,p(1) = 100/x.

Formula,
Profit =((s.p-c.p)*100/c.p
25=((100/x)-5)*100/5
By solving this you will get x = 16.

Simply using the formula:

SP = 100 + profit × CP/100.
CP : SP.
X: 20.
Simply putting the value you will get the 16 as answer.

Let cp=100 for 20 articles.
Profit=25%
Therefore, sp = 125.
Now for 125 - 20 articles,
100 - how many articles?
20 x 100/125 = 16.

So, 16 is the answer.

I am not getting how this 5/4 came. Anyone, please explain to me.