Aptitude - Problems on Numbers - Discussion

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.

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.

4xy is the right way. But,easy way is,

Sum of two numbers->x+y = 25..........1.

Difference of same two numbers->x-y = 13......2.

1&2 solve, 2x = 38.

x = 19.

Sub the value x in equation 1,

The value of y is 6.

Finally, the product of two numbers, x*y = 19*6 = 114.

(x+y)² = x² + y² + 2xy -----------(1)
(x-y)² = x² + y² - 2xy -----------(2)

Subtract (1) - (2) => (x+y)² - (x-y)² = 4xy...

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.

Another easy way is:

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

Solving it we get x=19.

Substituting x=19 in 1st equation,
We get y=6.
Product= xy =19*6=114.

I am a primary school student, I have a doubt, anyone please clarify this. How to solve this question without taking the unknown variable X & Y?

X+y=25,
X-y=13.
Then add both equation, we get 2x=38 (+y-Y=1), Hence X=38/2 = 19.

So X=19,
19+y=25.
y=25-19=>6.

So product of XY = 19*6 = 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.