| Directions: In the following questions two equations numbered I and II are given. You have to solve both the equations and give answer. |
| I. \[9x-15.45=54.55+4x\] |
| II. \[\sqrt{y+155}-\sqrt{36}=\sqrt{49}\] |
A) If \[x>y\]
B) If \[x\ge y\]
C) If \[x<y\]
D) If \[x\le y\]
E) If x = y or the relationship cannot be established
Correct Answer: E
Solution :
| I. \[9x-15.45=54.55+4x\] |
| \[\Rightarrow \] \[9x-4x=54.55+15.45\] |
| \[\Rightarrow \] \[5x=70\]\[\Rightarrow \]\[x=\frac{70}{5}\]\[\Rightarrow \]\[x=14\] |
| II. \[\sqrt{y+155}-\sqrt{36}=\sqrt{49}\] |
| \[\Rightarrow \] \[\sqrt{y+155}-6=7\] |
| On squaring both sides, we get |
| \[\Rightarrow \] \[{{(\sqrt{y+155})}^{2}}={{(13)}^{2}}\] |
| \[\Rightarrow \] \[y+155=169\] |
| \[\Rightarrow \] \[y=169-155\]\[\Rightarrow \]\[y=14\] |
| Hence, \[x=y\] |
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