If from twice the greater of two numbers 16 is subtracted, the result is half the other number. If from half the greater number 1 is subtracted, the result is still half the other number. What are the numbers?

Let the greater number be x and smaller number be y.

According to question if from twice the greater of two numbers 16 is subtracted, the result is half the other number.

∴ 2x - 16 = $\dfrac{y}{2}$

⇒ 2(2x - 16) = y

⇒ 4x - y = 32 …….(i)

According to question, if from half the greater number 1 is subtracted, the result is still half the other number.

$\therefore \dfrac{x}{2} - 1 = \dfrac{y}{2} \\[1em] \Rightarrow 2\Big(\dfrac{x}{2} - 1\Big) = y \\[1em] \Rightarrow x - y = 2 …….(ii)$

Subtracting eq. (ii) from eq. (i) we get,

⇒ 4x - y - (x - y) = 32 - 2

⇒ 4x -y - x + y = 30

⇒ 3x = 30

⇒ x = $\dfrac{30}{3}$

⇒ x = 10

Substituting value of x in (ii) we get,

10 - y = 2

⇒ y = 10 - 2

⇒ y = 8

Hence, two numbers are 8 and 10.