Question

The sum of two numbers is 25 & their difference is 7, then the numbers are.
A) 20, 5
B) 18, 7
C) 15, 10
D) 9, 16

Answer 1

Hint:In this problem, we have to find two numbers. Whose sum is 25 & the difference is 7. We can find two numbers by assuming them as a \[x\,\&\,y\].By given information we will make two equations. Then we find the values of \[x\,\&\, y\] by using these equations.

Complete step-by-step answer:
We have given the sum of two numbers is 25.
Let $x\,\&\,y$ be the two numbers
And they given sum of two numbers is 25,
So, here we have to add \[x\,\&\, y\] to make the equation.
We get the equation,
$x + y = 25 ......... (1)$
Now, the difference of two numbers is given as 7.
So, we get the equation.
$x - y = 7 ……...… (2)$
Now, we can find the value of \[x\,\&\, y\] by using these two above equations (1) & (2).
We can find the values by adding these two equations.
Let us do addition.
$x + y + x - y = 25 + 7$
Here, y will get cancelled. So, we get.
$2x = 32$
$ \Rightarrow x = 16$
Hence the value of x is 16.
Now, we can find the value of y by putting the value of x in the equation (1).
$x + y = 25$
$\therefore 16 + y = 25$
To find the value of y, subtract 16 from both the sides.
$ \Rightarrow 16 - 16 + y = 25 - 16$
$ \Rightarrow y = 9$
Hence we get the values $x = 16\,\&\,y = 9$
Let’s check the correctness of the answer by taking the sum of two derived answers, it should be 25.
$x + y = 25$
$16 + 9 = 25$
$\therefore 25 = 25$
Hence, our answers are correct.

So, the correct answer is “Option D”.

Note:The chances of mistakes are when solving the equations. Here we have to take care of signs. Note that, in any problem like this, whenever we find the values, we should start the solution by assuming them with any variable.