Madhya Pradesh Police Exam Model Paper 9

Given: Of three numbers, the second number is 5 more than the average of the first and the third number. The third number is 6 more than the first number.
Formula: Average of n numbers a1, a2, ..., an = (a1 + a2 + ... + an)/n
Calculation: Let the three numbers be a, b and c.
According to question
$\mathit{b}-\left(\mathit{a}+\mathit{c}\right)/2=5$
$\Rightarrow 2\mathit{b}\mathit{–}\mathit{a}\mathit{–}\mathit{c}=10$ ----(1)
And
$\mathit{c}\mathit{–}\mathit{a}=6$
$\Rightarrow \mathit{c}=\mathit{a}+6$
Put the value of c in equation (1) we get,
$2\mathit{b}\mathit{–}\mathit{a}\mathit{–}\left(\mathit{a}+6\right)=10$
$\Rightarrow 2\mathit{b}\mathit{–}\mathit{a}\mathit{–}\mathit{a}\mathit{–}6=10$
$\Rightarrow 2\mathit{b}\mathit{–}2\mathit{a}=16$
$\Rightarrow 2\left(\mathit{b}\mathit{–}\mathit{a}\right)=16$
$\Rightarrow \mathit{b}\mathit{–}\mathit{a}=8$
∴ difference between first and second no. is 8.