Question

Of the three numbers, the sum of the first two is 45, the sum of second and third is 55 and the sum of third and thrice of the first is 90. The third number is:

Answer 1

Let the three numbers be x and y and z

According to question :-

$x + y = 45 \\ \\ y +z = 55 \\ \\z + 3x = 90$

Solving first two equations :-

$x + y = 45 \\ z + y = 55 \\ - \: \: - \: \: \: \: - \\ = = = = = = = = = \\ x - z = ( - 10).......(iv)$

Now solving equation 3 and 4 :-

$3x + z = 90 \\ x - z = ( - 10) \\ \\ = = = = = = = = = = \\4x = 80 \\ \\x = 20 \\ \\ \\ \\z = x + 10 = 30 \\ \\ \\ \\y = 55 - z = 25$

Hence,

The three numbers are 20,25 and 30.

Thus

The third number is 30