Question

The sum of two numbers is \[100\] and their difference is \[50\]. Then the ratio of the two numbers is
A. \[2:1\]
B. \[3:1\]
C. \[4:1\]
D. \[5:1\]

Answer 1

Hint: Here to find the ratio of two unknown terms, consider any two random variables and form the equations as per the given statements in the question. Let \[x\] and\[y\]be the two numbers. The sum is \[x + y = 100\] and the difference is \[x - y = 50\].

Complete step-by-step solution:
We need to consider any random variables for the two numbers.
For this let us consider \[x\] and \[y\] are the two numbers.
As mentioned in the question the sum of two numbers is \[100\]
\[\Rightarrow x + y = 100\] …………………………….1
The difference of two numbers is \[50\]
\[\Rightarrow x - y = 50\] ...……………………………2
Now, adding equation 1 and 2
\[\Rightarrow x + y = 100\]
\[\Rightarrow x - y = 50\]
We get,
\[\Rightarrow 2x = 150\]
Therefore, the value of \[x\] we get
\[\Rightarrow x = 75\]
Next, we need to find the value of \[y\].
Hence, to find the value of \[y\] put the value of \[x\] in equation 1
As we know equation 1 is
\[\Rightarrow x + y = 100\]
We have calculated the value of \[x\] as \[x = 75\]
Substituting the value, we get
\[\Rightarrow x + y = 100\]
\[\Rightarrow 75 + y = 100\]
\[\Rightarrow y = 25\]
Therefore, the values of \[x\] and \[y\] are
\[x = 75\] and \[y = 25\]
Hence, we need to find the ratio of these two numbers
\[x:y\]
Substitute the values of \[x\] and \[y\]
\[\Rightarrow 75:25\]
The ratio is
\[\Rightarrow 3:1\]
Therefore,
\[\Rightarrow x:y = 3:1\]
Therefore, option \[B\] is the right answer for this question.

Note: To find any values for these types of statements we need to consider any random variables as the unknown number, 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.