If 45 is subtracted from twice the greater of two numbers, it results in the other number.

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

Then, we have: 

25x – 45 = y or 2x – y = 45 ……….(i) 

2y - 21 = x or –x +2y = 21 ………(ii) 

On multiplying (i) by 2, we get: 

4x - 2y = 90 ………..(iii) 

On adding (ii) and (iii), we get 

3x = (90 + 21) = 111 

⇒ x = 37 

On substituting x = 37 in (i), we get 

2 × 37 - y = 45 

⇒ 74 - y = 45 

⇒ y = (74 - 45) = 29 

Hence, the greater number is 37 and the smaller number is 29.

Let us consider,

First greater number = x and

Second smaller number = y

As per the statement,

2x – 45 = y …(1)

2y – 21 = x …(2)

Using Substitution method:

Substituting the value of y in (2),

2 (2x – 45) – 21 = x

4x – 90 – 21 = x

4x – x = 111

3x = 111

x = 37

From (1): y = 2 x 37 – 45 = 29

Answer:

The numbers are 37 and 29.

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

Then, we have: 

25x – 45 = y or 2x – y = 45 ……….(i) 

2y - 21 = x or –x +2y = 21 ………(ii) 

On multiplying (i) by 2, we get: 

4x - 2y = 90 ………..(iii) 

On adding (ii) and (iii), we get 

3x = (90 + 21) = 111 

⇒ x = 37 

On substituting x = 37 in (i), we get 

2 × 37 - y = 45 

⇒ 74 - y = 45 

⇒ y = (74 - 45) = 29 

Hence, the greater number is 37 and the smaller number is 29.