Question

The sum of two numbers is 100 and one number is two less than twice the other number. Then the numbers are
A.34,66
B.34,76
C.44,56
D.46,54

Answer 1

Hint: In this question, we need to evaluate the value of both the numbers such that the sum of two numbers is 100 and one number is two less than twice the other number. For this, we need to establish the relation between the numbers following the given conditions and then, solve the equations simultaneously to get the result.

Complete step-by-step answer:
Let the two numbers be ‘x’ and ‘y’ respectively.
According to the question, the sum of the numbers is 100. So, we can write
 $ x + y = 100 - - - - (i) $
Also, it has been given that one number is two less than twice the other number. So, mathematically we can write it as:
 $ x = 2y - 2 - - - - (ii) $
Substituting the expression of the parameter ‘x’ from the equation (ii) in the equation (i), we get
\[
  x + y = 100 \\
   \Rightarrow 2y - 2 + y = 100 \\
   \Rightarrow 3y = 100 + 2 \\
   \Rightarrow y = \dfrac{{102}}{3} \\
   \Rightarrow y = 34 \;
 \]
So, the value of one of the two numbers is 34.
Now, substituting the value of the variable ‘y’ in the equation (ii) to determine the value of the parameter ‘x’, we get
 $
  x = 2y - 2 \\
   \Rightarrow x = 2 \times 34 - 2 \\
   \Rightarrow x = 68 - 2 \\
   \Rightarrow x = 66 \;
  $
Hence, the value of the other number is 66.
Therefore, the two numbers satisfying the given condition are 34 and 66.
Option A is correct.
So, the correct answer is “Option A”.

Note: It is worth noting down here that all the conditions given in the given variables must be satisfied so as to get the desired result correctly and so, it all depends on the language of the problem and how we grasp it. Students may also go through the options to get the answer but that is time consuming.