Three numbers which are co-prime to one another are such that product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is = ?

Solution(By Examveda Team)

$$\eqalign{ & {\text{Let number are }}a,{\text{ }}b,{\text{ }}c \cr & {\text{ = }}a,{\text{ }}b,{\text{ }}c{\text{ are co - prime numbers}} \cr & {\text{HCF (}}a,b,c{\text{) = 1}} \cr & \Rightarrow \frac{{a \times b}}{{b \times c}} = \frac{{1073}}{{551}} = \frac{{37 \times 29}}{{17 \times 29}} \cr & \Rightarrow \frac{a}{c} = \frac{{37}}{{19}} \cr & \Rightarrow {\text{Common }}b{\text{ factor is cancel out}}{\text{.}} \cr & \therefore a = 37,\,b = 29,\,c = 19 \cr & \therefore {\text{Sum of numbers}} \cr & {\text{ = }}a + b + c \cr & = 37 + 29 + 19 \cr & = 85 \cr} $$