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Question

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

3

5

7

11

ANSWER : 3

Descrption

<p style="margin-left:0px;"><strong>Solution(By Examveda Team)</strong></p><p><strong>According to the question,</strong><br><strong>&nbsp;</strong></p><p style="margin-left:0em;"><strong>⇒x+y+z/3=45</strong></p><p style="margin-left:0em;"><strong>⇒x+y+z=135.....(i)</strong></p><p style="margin-left:0em;"><strong>⇒x-9=y+z/2</strong></p><p style="margin-left:0em;"><strong>⇒2x−y−z=18.....(ii)</strong></p><p style="margin-left:0em;">&nbsp;</p><p style="margin-left:0em;"><strong>now(i)+(ii)</strong></p><p style="margin-left:0em;"><strong>x+y+z=135</strong></p><p style="margin-left:0em;"><strong>2x-y-z=18</strong></p><p style="margin-left:0em;"><strong>________________</strong></p><p style="margin-left:0em;"><strong>3x=153</strong></p><p style="margin-left:0em;"><strong>x=51</strong></p><p><br><strong>From (i)</strong><br><strong>y + z = 135 - 51 = 84.....(iii)</strong><br><strong>Also,</strong><br><strong>&nbsp;</strong></p><p style="margin-left:0em;"><strong>⇒y+z/2=y+2</strong></p><p style="margin-left:0em;"><strong>⇒y+z=2y+4</strong></p><p style="margin-left:0em;"><strong>⇒-y+z=4…….(iv)</strong></p><p style="margin-left:0em;"><strong>now, (iii)+(iv)</strong></p><p style="margin-left:0em;"><strong>&nbsp; y+z=84</strong></p><p style="margin-left:0em;"><strong>-y+z=4</strong></p><p style="margin-left:0em;"><strong>_________</strong></p><p style="margin-left:0em;"><strong>2z=88</strong></p><p style="margin-left:0em;"><strong>⇒ z=44</strong></p><p><br><strong>Required difference</strong><br><strong>= 51 - 44 = 7</strong></p>

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