A number is as much greater than 36 as is less than 86. Find the number.

Let the required number be x.

"As much greater than 36" means: (x - 36)

"As is less than 86" means: (86 - x)

Since these two differences are equal:

∴ x - 36 = 86 - x

⇒ x + x = 86 + 36 $\quad$ [Transposing -36 to RHS and -x to LHS]

⇒ 2x = 122

⇒ x = $\dfrac{122}{2}$

⇒ x = 61

Hence, the required number is 61.