There are 4 consecutive odd numbers (x₁, x₂, x₃ and x₄) and three consecutive even numbers (y₁, y₂ and y₃). The average of odd numbers is 6 less than average of even numbers. If sum of three even numbers is 16 less than sum of four odd numbers, what is average of x₁, x₂, x₃ and x₄?

According to given information
Average of odd numbers = Average of even numbers - 6
$$ \Rightarrow \frac{{{x_1} + {x_2} + {x_3} + {x_4}}}{4} = $$     $$\frac{{{y_1} + {y_2} + {y_3}}}{3} - 6$$
$$ \Rightarrow \frac{{{x_1} + {x_2} + {x_3} + {x_4}}}{4} = $$     $$\frac{{{y_1} + {y_2} + {y_3} - 18}}{3}$$
$$ \Rightarrow 3\left( {{x_1} + {x_2} + {x_3} + {x_4}} \right) = $$     $$4\left( {{y_1} + {y_2} + {y_3}} \right) - 72$$
Also,
$$ \Rightarrow {y_1} + {y_2} + {y_3} = $$     $${x_1} + {x_2} + {x_3} + {x_4} - 16$$
$$ \Rightarrow {x_1} + {x_2} + {x_3} + {x_4} = $$     $${y_1} + {y_2} + {y_3} + 16$$   .....(i)
So we have,
$$ \Rightarrow 3\left( {{y_1} + {y_2} + {y_3} + 16} \right) = $$     $$4\left( {{y_1} + {y_2} + {y_3}} \right) - 72$$
$$ \Rightarrow 3{y_1} + 3{y_2} + 3{y_3} + 48 = $$     $$4{y_1} + 4{y_2} + 4{y_3} - 72$$
$$ \Rightarrow 4{y_1} + 4{y_2} + 4{y_3}$$   $$ - 3{y_1} - 3{y_2} - 3{y_3}$$     = 48 + 72
$$ \Rightarrow {y_1} + {y_2} + {y_3} = 120$$
$$ \Rightarrow {x_1} + {x_2} + {x_3} + {x_4}$$     = 120 + 16 = 136 [From (i)]
? Average of four odd numbers :
$$\eqalign{ & = \frac{{{x_1} + {x_2} + {x_3} + {x_4}}}{4} \cr & = \frac{{136}}{4} \cr & = 34 \cr} $$