In a set of three numbers, the average of first two numbers is 2, the average of the last two numbers is 3, and the average of the first and the last numbers is 4. What is the average of three numbers?
A. 2
B. 2.5
C. 3
D. 3.5
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{three}}\,{\text{numbers}}\,{\text{be}}\,x,\,y,\,{\text{and}}\,z.\, \cr & {\text{We}}\,{\text{are}}\,{\text{given}}\,{\text{that}}\, \cr & \frac{{ {x + y} }}{2} = 2 \cr & \frac{{ {y + z} }}{2} = 3 \cr & \frac{{ {x + z} }}{2} = 4 \cr & {\text{Adding}}\,{\text{three}}\,{\text{equations}}, \cr & \frac{{ {x + y} }}{2} + \frac{{ {y + z} }}{2} + \frac{{ {x + z} }}{2} = 2 + 3 + 4 \cr & x + y + z = 9 \cr & {\text{The}}\,{\text{average}}\,{\text{of}}\,{\text{the}}\,{\text{three}}\,{\text{numbers}}\,{\text{is}}, \cr & \frac{{ {x + y + z} }}{3} = \frac{9}{3} = 3 \cr} $$Related Questions on Average
A. 125 km/hr
B. 75 km/hr
C. 135 km/hr
D. 120 km/hr
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