Aptitude - Problems on Numbers - Discussion

Why we are taking x+y and x-y, and another doubt is why we have to take 4xy?

Please clarify this term.

Please, can anyone explain this in easy way?

X+Y = 25... (1)
X-Y = 13...(2)

when we add this we get X = 19... But how see below..
lets take two numbers as X and Y... then..
sum of two number is 25... means X + Y = 25..
and their difference is 13... means X - Y = 13...
but when we add both...

X + Y = 25
+ X - Y = 13
------------------
2X = 38.........

(+Y and -Y gets substracted so above X plus below X is equal to 2X and 25+13 equals to 38)

when we get 2X = 38 then.
X = 38/2 = 19
then if X + Y = 25 then....
19 + Y = 25
Y = 25 - 19 = 6...
we get X = 19 and Y = 6 then.

Find their product... means X * Y = ?
X * Y = 19 * 6 = 114
So Product for this is equal to 114.

Add 25+13=38
Sub. 25-13=12
Then we Wii take the ratio
38:12 which is
19:6
After multiple(19*6=114) these no. We will get 114.

x+y=25 ---> (1)
x-y=13--> x=13+y ---> (2).

Now insert (2) in (1)
=13+y+y=25,
=13+2y=25,
=2y=25-13,
=2y=12,
::y=6.

Now take eq (1).
x+6=25,
x=19,
now x*y=19*6=114.

x+y=25 -----------> 1.
x-y=13 ------------> 2.
-----------------------------
2x=38.

So, x=19,
When x=19, y=6(because x+y=25,y=25-x).
And then, xy=114.

@All.

x+y=25.
x-y=13----->1
x= 13 + y.
So,
13 + y + y =25..
13 + 2y =25
2y=25 - 13
2y= 12
y=12/2
y=6.

x+6=25.
x=25 - 6
x=19.

xy=19*6=114.

How 4xy? Please explain me.

4ab = (a+b)^2 - (a-b)^2.
4ab = 25^2 - 13^2.
= 625 - 169.
4ab = 456
ab = 456/4
= 114.

Let the two numbers be x and y.
The sum of two numbers is 25, which is:
x + y = 25 and, their difference is 13, which is:
x - y = 13.
So, when we subtract the sum and the difference we get;
x + y = 25,
-(x – y) = 13,
2y = 12,
y = 6.
Since, x + y = 25.
x + 6 = 25,
x = 25 - 6,
x = 19.
So, their product is x*y which is:
19 * 6 = 114(the answer).

Hope it helped.