Of the three numbers, the sum of the first two is 55, sum of the second and third is 65, and sum of third with thrice of the first is 110. The third number is -

Solution (By Examveda Team)

$$\eqalign{ & {\text{Let the 3 numbers be }}x,y,\& \,\,z \cr & {\text{According to question}} \cr & x + y = 55 \to y = 55 - x \cr & y + z = 65 \to 55 - x + z = 65 \cr & z - x = 10.....(i) \cr & z + 3x = 110.....(ii) \cr & {\text{Solve (i)}}\,{\text{and (ii)}} \cr & {\bf{z = 35,}} \cr & x = 25, \cr & y = 30 \cr} $$