Question

Mark the correct alternative in the following question:

The sum of three consecutive odd numbers is 81. The middle number is

(a) 25 (b) 27 (c) 31 (d) 29

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{three}\mathrm{consecutive}\mathrm{odd}\mathrm{numbers}\mathrm{be}x,x+2\mathrm{and}x+4. \\ \mathrm{As},\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{the}\mathrm{three}\mathrm{consecutive}\mathrm{numbers}\mathrm{is}81. \\ \Rightarrow x+\left(x+2\right)+\left(x+4\right)=81 \\ \Rightarrow 3x+6=81 \\ \Rightarrow 3x=81-6\left(\mathrm{By}\mathrm{transposing}6\mathrm{to}\mathrm{RHS}\right) \\ \Rightarrow 3x=75 \\ \Rightarrow x=\frac{75}{3}\left(\mathrm{By}\mathrm{transposing}3\mathrm{to}\mathrm{RHS}\right) \\ \Rightarrow x=25 \\ \therefore x+2=25+2=27 \end{gathered}$$

So, the middle number is 27.

Hence, the correct alternative is option (b).