Question

The average of \[2,\ 7,\ 6\ \] and \[x\] is \[5\] and the average of \[18,\ 1,\ 6,\ x\] and \[y\] is \[10\]. What is the value of\[{\ y}\]?
A). \[10\]
B). \[20\]
C). \[30\]
D). \[18\]

Answer 1

Hint: In this question, first given that the average of \[2,7,6\ \] and \[x\] is \[5\]. Here we need to find the value of \[x\]. Then also given that the average of \[18,1,6,x\] and \[y\] is \[10\] . After finding the value of \[x\], we need to substitute the value of \[x\] in the second statement and we need to find the value of\[{\ y}\].
Formula used :
\[\text{Average} = \dfrac{\text{Sum of observations}}{\text{The total number of observations}}\]

Complete step-by-step solution:
According to the question,
Given that the average of \[2,7,6\] and \[x\] is \[5\]
\[\text{Average}= \dfrac{2 + 7 + 6 + x}{4}\]
By substituting the values of average,
We get,
\[5 = \dfrac{\left( 2 + 7 + 6 + x \right)}{4}\]
By cross multiplying,
We get
\[20 = \left( 2 + 7 + 6 + x \right)\]
By simplifying,
We get
\[20 = 15 + x\]
 \[x = 20 – 15\]
By subtracting,
We get,
\[x = 5\]
Thus we get the value of \[x\] as \[5\]
Now by using the value of \[x\], we can find the value of \[y\]
According to the question,
The average of \[18,1,6,x\] and \[y\] is \[10\]
 \[average = \dfrac{\left( 18 + 1 + 6 + x + y \right)}{5}\]
By substituting the value of \[x\] and the average value,
We get,
\[10 = \dfrac{18 + 1 + 6 + 5 + y}{5}\] By simplifying,
We get,
\[10 = \dfrac{30 + y}{5}\]
 By cross multiplying,
We get,
\[50 = 30 + y\]
 \[50 – 30 = y\]
By subtracting,
We get,
\[y = 20\]
Thus we get the value of \[y\] is \[20\]
Final answer :
The value of \[y\] is \[20\]
Option : B). \[20\]

Note: The average is nothing but the sum of the values divided by the total number of values. Average is also known as arithmetic mean. In order to calculate the average, we need to add all the numbers given and divide by how many numbers present there.