question_answer

Directions: In the following questions, two equations numbered I and II are given. You have to solve both the equations and give answer                                                                          [IBPS RRB (Office Assistant) 2012]

I. \[4x+3y={{(1600)}^{1/2}}\]

II. \[6x-5y={{(484)}^{1/2}}\]

A) If \[x>y\]

B) If \[x\ge y\]

C) If \[x<y\]                      

D) If \[x\le y\]

E) If \[x=y\]or relationship cannot be established

Correct Answer: A

Solution :

I. \[4x+3y={{(1600)}^{1/2}}\]

\[\Rightarrow \]   \[4x+3y=40\]                            ... (i)

II.  \[6x-5y={{(484)}^{1/2}}\]

\[6x-5y=22\]                              ... (ii)

On multiplying Eq. (i) by 6 and Eq, (ii) by 4, we get

\[y=\frac{152}{38}=4\]

On putting the value of y in Eq. (ii), we get

\[6x-5\,\,(4)=22\]

\[\Rightarrow \]               \[6x=22+20\]\[\Rightarrow \]\[6x=42\]

\[\therefore \]                  \[x=7\]

Hence,               \[x>y\]