Aptitude - Problems on Numbers - Discussion

14. 

The sum of two number is 25 and their difference is 13. Find their product.

[A]. 104
[B]. 114
[C]. 315
[D]. 325

Answer: Option B

Explanation:

Let the numbers be x and y.

Then, x + y = 25 and x - y = 13.

4xy = (x + y)2 - (x- y)2

   = (25)2 - (13)2

   = (625 - 169)

   = 456

xy = 114.


Shyam said: (Feb 5, 2011)  
Find the value of the variable X and Y separately and find the product of both.

Veena said: (Feb 23, 2011)  
How 4xy?

Prashanth said: (Mar 20, 2011)  
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

Manikandan said: (Apr 21, 2011)  
hi Prashanth it is good....

Vaishu said: (May 16, 2011)  
How 4xy?

Manjunathyadav said: (May 21, 2011)  
HOW 4XY HAS COME?

Manikumar said: (May 25, 2011)  
Every One Just follows Prashanth one.

Karthika said: (Jul 2, 2011)  
(x+y)2 = x2 + y2 + 2xy -----------(1)
(x-y)2 = x2 + y2 - 2xy -----------(2)

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

Lucky said: (Jan 1, 2013)  
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.

Subi said: (Mar 15, 2013)  
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.

Mahesh said: (Jul 9, 2013)  
x+y=25.......1.
x-y=13.......2.

Add 1&2

2x = 38,
x = 19 (now substitute x val in 1).

19+y = 25.
y = 6.

x*y = 19*6.
= 114.

Kowselya said: (Aug 18, 2013)  
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.

Deepakamal said: (Oct 9, 2013)  
x+y = 25 and
x-y = 13.

To solve this we can get x=19 and y=6.

But the question is product of two no.

So, xy = 19x6 = 114 is the answer

Hitesh said: (Jun 25, 2014)  
Why taken 4xy?

Jayesh Bro, said: (Jun 1, 2015)  
How 4xy?

Ans: Because there two number is 25 & for that's 2+.

(X+Y-X-Y=2xy).

That's why 2+2xy=4xy.

Charles said: (Jul 24, 2015)  
Thanks guys.

Tanishqa said: (Jun 1, 2016)  
How to substitute the value of x and y?

Kakali Tripathi said: (Jul 21, 2016)  
Thanks @Prashanth.

Devendra said: (Jul 22, 2016)  
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?

Lav said: (Nov 3, 2016)  
x + y = 25.
x - y = 13.

2x = 12.
x = 6.
y = 19.
xy = 114.

Priya said: (Dec 20, 2016)  
Why we are taking x+y and x-y, and another doubt is why we have to take 4xy?

Please clarify this term.

Smita said: (Mar 3, 2017)  
Please, can anyone explain this in easy way?

Mayur Patil said: (May 18, 2017)  
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.

Ganesh said: (Sep 25, 2017)  
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.

Shashi said: (Jun 14, 2018)  
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.

Yoon Darli said: (Sep 27, 2018)  
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.

Anonymous said: (Jun 1, 2019)  
@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.

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