If from twice the greater number of the two numbers, 45 is subtracted, the result is the other number. If from twice the smaller number, 21 is subtracted, the result is the greater number. Find the numbers.

Let two numbers be x and y, where x > y.

Given,

If from twice the greater number of the two numbers, 45 is subtracted, the result is the other number.

⇒ 2x - 45 = y     …..(1)

Given,

If from twice the smaller number, 21 is subtracted, the result is the greater number.

⇒ 2y - 21 = x     …..(2)

Substituting value of y from equation (1) in (2), we get :

⇒ 2y - 21 = x

⇒ 2(2x - 45) - 21 = x

⇒ 4x - 90 - 21 = x

⇒ 4x - x - 111 = 0

⇒ 3x = 111

⇒ x = $\dfrac{111}{3} = 37.$

Substituting value of x in equation (1), we get :

⇒ 2x - 45 = y

⇒ 2(37) - 45 = y

⇒ 74 - 45 = y

⇒ y = 29.

Hence, the numbers are 37 and 29.