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SSC Sample Paper SSC CGL - Sample Paper-17

  • question_answer
    The average of the three numbers x, y and z is 45. x is greater than the average of y and z by 9. The average of y and z is greater than y by 2. Then, the difference of x and z is

    A) 3                                 

    B) 5        

    C) 7                     

    D) 11

    Correct Answer: C

    Solution :

    \[x+y+z=3\times 45=135\] \[x=\frac{y+z}{2}+9\]                          ?(i) \[\Rightarrow \]   \[2x-y-z=18\]                             ...(ii) and       \[\frac{y+z}{2}=y+2\] \[\Rightarrow \]   \[y+z=2y+4\] \[\Rightarrow \]   \[z-y=7\]                                    ?(iii) By Eqs. (i) + (ii),             \[3x=135+18=153\] \[\Rightarrow \]   \[x=51\] By Eqs. (i) and (iii),             \[x+y+z+z-y\]             \[=135+4=139\] \[\Rightarrow \]   \[x+2z=139\] \[\Rightarrow \]   \[51+2z=139\] \[\Rightarrow \]   \[2z=139-51=88\]          \[\therefore \]      \[z=44\] \[\therefore \]      \[x-z=51-44=7\]


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