Question

The sum of three numbers is 20. If we multiply the first by 2 and add the second number and subtract the third we get 23. If we multiply the first by 3 and add second and third to it, we get 46. By using rank method find the numbers.

Answer 1

Let the three number be x, y and z respectively. 

According to the problem, 

x + y + z = 20 

2x + y – z = 23 

3x + y + z = 46 

The matrix equation is given by

x + y + z = 20 …….. (1) 

-y – 3z = -17 …….. (2) 

4z = 20 …….. (3) 

(3) ⇒ z = 5 

(2) ⇒ -y = -17 + 3(5) = -2 ⇒ y = 2 

(1) ⇒ x = 20 – 2 – 5 = 13 

Hence the three numbers are (13, 2, 5)