Question

The sum of two numbers is 22. Five times of one number is equal to 6 times the other. The bigger of the two numbers is
A) 10
B) 12
C) 15
D) 16

Answer 1

Hint: To solve this question first of all we will assume one of the numbers as x and then according to given conditions of the question will make equations in the variable x and then will solve it to get the desired result.

Complete step-by-step answer:
Given that the sum of two numbers is 22. Also, that five times of one number is equal to 6 times of another number.
We have to find the value of a bigger number.
Let one number is x.
Now because it is given that the sum of both the numbers is 22. So, the other number would be (22-x).
Again given in the question that five times of one number is equal to 6 times of another.
Now using the above condition we get,
\[5x=6(22-x)\]
Now solving the above obtained expressions using necessary rearrangements we get,
\[\begin{align}
  & 5x=6(22-x) \\
 & \Rightarrow 5x=132-6x \\
 & \Rightarrow 5x+6x=132 \\
 & \Rightarrow 11x=132 \\
 & \Rightarrow x=\dfrac{132}{11} \\
 & \Rightarrow x=12 \\
\end{align}\]
Therefore, we obtain one number as x = 12.
Then calculating the value of the other number, we get,
(22-x) = (22-12) = 10.

Hence, we obtained both numbers as 12 and 10. The Bigger number of them is 12.
Therefore, we get the required result as 12.

Note: The possibility of error in these types of question can be at the point where you are assuming a variable to determine the given number. In such conditions always assume one variable and try to manipulate the second number in terms of the first variable itself. Do not go for assuming two different variables for the two different numbers.