Question

The difference of two numbers is \[45\]. The larger number is \[5\] more than \[2\]times the smaller number. Find the numbers
A. \[92\]and \[49\]
B. \[98\]and \[40\]
C. \[92\] and \[48\]
D. \[95\] and \[40\]

Answer 1

Hint:As we know sum is result of adding two or more numbers and difference is result of subtracting two or more numbers and hence, here we need to find the two unknown terms of the given difference, for this consider any two random variables and write the equations as per the given statements in the question.

Complete step by step answer:
For any given unknown term in the question, we need to consider any random variables for the unknown term. As mentioned in the question the difference of two numbers is \[45\] for this let us consider \[x\] and \[y\] are the two variables hence, we get
\[x - y = 45\] ………………………………………(1)
where, \[x\] and \[y\] are the two numbers which we considered.
As per the question the larger number is \[5\] more than \[2\] times the smaller number, by this we get
\[x = 5 + 2y\] ……………………………………(2)
Next put the value of \[x\] in equation 1 Then, the equation 1 becomes
\[5 + 2y - y = 45\]
Further simplifying we get
\[y = 45 - 5\]
Hence,
\[y = 40\]
Now substitute the value of \[y\] in equation 1, we get
\[x - 40 = 45\]
To find the value of x rearrange the terms, hence we get
\[x = 45 + 40\]
\[\Rightarrow x = 95\]
After solving we got the value as \[x = 95\]. Hence, the values of \[x\] and \[y\] we got after calculating are \[95\] and \[40\].

Therefore, option D is the correct.

Note: To find any values for these types of statements we need to consider any random variables as the unknown term, next solving as per the statements stated we can find out the values of any number asked. If they asked to find three numbers then consider \[x,y,z\] as the unknown variables and solve the sum.