# Aptitude - Problems on Numbers - Discussion

### Discussion :: Problems on Numbers - General Questions (Q.No.14)

14.

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

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

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.