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1. Of the three number, the sum of the first two is 73, the sum of the second and the third is 77 and the sum of the third and thrice the first is 104. The third number is ?

A. 25

B. 39

C. 48

D. Cannot be determined

Solution:

Let the numbers be x, y and z
Then,

\begin{aligned} x + y = 73 \\ \Leftrightarrow y = 73 - x \\ y + z = 77 \\ \Leftrightarrow z = 77 - y \\ \Leftrightarrow z = 77 - (73 - x) \\ \Leftrightarrow z = 4 + x \\ 3 x + z = 104 \\ \Leftrightarrow 3 x + 4 + x = 104 \\ \Leftrightarrow 4 x = 100 \\ \Leftrightarrow x = 25 \\ ∵ y = (73 - 25) \\ \Leftrightarrow y = 48 \\ ∵ z = (4 + 25) \\ \Leftrightarrow z = 29 \end{aligned}

∴ Third number = 29

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