10th Class Mathematics Pair of Linear Equations in Two Variables Question Bank MCQs - Pair of Linear Equations in Two Variables

The length of a room exceeds its breadth by\[3m\]. If the Length is increased by \[3m\] and the breadth is decreased by \[2m,\] the area remains the same. Find the length and the breadth of the room.

A) \[12m,\,9m\]

B) \[17m,\,14m\]

C) \[15m,\,12m\]

D) \[14m,\,11m\]

Correct Answer: C

Solution :

[c] Let length of the room is x m and breadth is y m.

Then, \[x=y+3\,\,\Rightarrow \,\,\,x-y=3\] ...(1)

and \[(x+3)\,\,(y-2)=xy\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,-2x+3y=6\] ...(2)

Multiplying eq. (1) by 2, we get

\[2x-2y=6\] ...(3)

On adding eqs. (2) and (3), we get \[y=12\]

Substituting \[y=12\]in eq. (1), we get

\[x=12+3=15\]

Hence, the length and breadth of the room are 15 m and 12 m respectively.