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1. 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 = ?

A. 75

B. 81

C. 85

D. 89

Solution:

\begin{aligned} Let number are a, b, c \\ = a, b, c are co - prime numbers \\ HCF (a, b, c)  =  1 \\ \Rightarrow \frac{a \times b}{b \times c} = \frac{1073}{551} = \frac{37 \times 29}{17 \times 29} \\ \Rightarrow \frac{a}{c} = \frac{37}{19} \\ \Rightarrow Common b factor is cancel out . \\ ∴ a = 37, b = 29, c = 19 \\ ∴ Sum of numbers \\ = a + b + c \\ = 37 + 29 + 19 \\ = 85 \end{aligned}

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