Question

Mark the correct alternative in the following question:

A number is as much greater than 31 as it is less than 81. The number is

(a) 46 (b) 56 (c) 66 (d) 76

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{number}\mathrm{be}x. \\ \mathrm{As},\mathrm{the}\mathrm{number}\mathrm{is}\mathrm{as}\mathrm{much}\mathrm{greater}\mathrm{than}31\mathrm{as}\mathrm{it}\mathrm{is}\mathrm{less}\mathrm{than}81. \\ \Rightarrow x-31=81-x \\ \Rightarrow x+x=81+31\left(\mathrm{By}\mathrm{transposing}-x\mathrm{to}\mathrm{LHS}\mathrm{and}-31\mathrm{to}\mathrm{RHS}\right) \\ \Rightarrow 2x=112 \\ \Rightarrow x=\frac{112}{2}\left(\mathrm{By}\mathrm{transposing}2\mathrm{to}\mathrm{RHS}\right) \\ \therefore x=56 \end{gathered}$$

So, the number is 56.

Hence, the correct alternative is option (b).