Question

The sum of the number and its half is 84. Number will be
A.65
B.56
C.66
D.None of these

Answer 1

Hint: Let the given number be x and use the condition given in the question that the sum of the number and it’s half is 84. Hence form the equation using the above given condition and proceed to find the unknown number.

Complete step-by-step answer:
Let the number be x and half of number be \[\dfrac{x}{2}\]
Using the condition given in the question we can make the equation as below:
\[ \Rightarrow \]\[\dfrac{x}{2} + x = 84\] …(1)
\[ \Rightarrow \]\[\dfrac{{3x}}{2} = 84\]
\[ \Rightarrow \]\[3x = 168\]
\[ \Rightarrow \]\[x = 56\]
Hence on solving (1), \[x = 56\] is obtained and option (b) is the correct answer.

Note: Another approach to solve this question can be by options,
Given that one half of a number is 84
So directly we can say that 84 is 1.5 times a number
Option a is 65
So \[65\left( {1.5} \right) = 97.5\]which is not equal to 84
Option b is 56
So \[56\left( {1.5} \right) = 84\]
Hence 56 is the required number.