Question

The sum of two numbers is 3 and their difference is 1. Find the numbers.
\[\begin{align}
  & A.\text{ }2\text{ }and\text{ }-1 \\
 & B.\text{ }2\text{ }and\text{ }1 \\
 & C.\text{ }-2\text{ }and\text{ }1 \\
 & D.\text{ }1\text{ }and\text{ }2 \\
\end{align}\]

Answer 1

Hint: In this question, we have to find two numbers whose sum and difference is given. For finding the required answer, we will first suppose the two numbers as some variable and then form two equations. One equation will be formed by adding the variables and keeping them equal to 3 whereas the other equation will be formed by subtracting any one variable from another and keeping it equal to 1. At last will solve the obtained two equations to get the value of variables which will be our required answer.

Complete step-by-step answer:
Here, we have to find two numbers whose sum is 3 and difference is 1. Let us suppose these numbers as some variables.
Let us suppose that two numbers are x and y. We are given sum of number as 3, therefore, we can write equation as
\[x+y=3\cdots \cdots \cdots \cdots \left( 1 \right)\]
Now, we are also given the difference of these numbers as 1. Let us consider that, x is greater than y, therefore equation becomes,
\[x-y=1\cdots \cdots \cdots \cdots \left( 2 \right)\]
We have obtained two equations (1) and (2). Solving them will give us value of variables. So, let us solve them. Let us first add the equation so that y cancels out, we get:
\[\begin{align}
  & x+y+x-y=3+1 \\
 & \Rightarrow 2x=4 \\
\end{align}\]
Dividing both sides by 2, we get:
\[x=2\]
Now, let us put this value of x in equation (1) to obtain value of y, we get:
\[2+y=3\]
Taking 2 to other side, we get:
\[\begin{align}
  & y=3-2 \\
 & \Rightarrow y=1 \\
\end{align}\]
Hence, we have found values of variable as x = 2 and y = 1.
So, our required numbers are 1 and 2.

So, the correct answer is “Option B”.

Note: Students should note that we have supposed x to be greater than y because if x was smaller than difference (x-y) cannot be positive and hence to make x-y as positive, x is greater than y. While adding two equations, the left side of both equations are added separately and the right side of both equations are added separately. To avoid confusion, students can take constant terms on the left side so that the right side becomes zero. After finding the value of x, we can put the value of x into any of the equations to find the value of y.