Algebra

Matrices & Determinants

Medium

Manjeet wants to donate a rectangular plot of land for a school in his village. When he has asked to give dimensions of the plot, he told that if its length is decreased by 50 m and breadth is increased by 50 m, then its area will remain same, but if its length is decreased by 10 m and breadth is decreased by 20 m, then its area will decrease by 5300 $m^2$ . If length and breadth of the plot are $x$ and $y$ respectively, then based on above information answer the question.

The length ( $x$ ) and breadth ( $y$ ) of plot satisfy equations:

$x - y = 50$ , $2x - y = 550$

$x - y = 50$ , $2x + y = 550$

$x + y = 50$ , $2x + y = 550$

✅ Correct Option: 2

First condition: $(x-50)(y+50) = xy \Rightarrow xy + 50x - 50y - 2500 = xy \Rightarrow x - y = 50$ . Second condition: $(x-10)(y-20) = xy - 5300 \Rightarrow xy - 20x - 10y + 200 = xy - 5300 \Rightarrow 20x + 10y = 5500 \Rightarrow 2x + y = 550$ . So the equations are $x - y = 50$ and $2x + y = 550$ .

Question 47

The linear equation involving $x$ and $y$ are written in matrix form as:

Question 48

The length of the plot is:

Question 49

The breadth of plot is:

Question 50

Area of the rectangular plot is:

The length (xxx) and breadth (yyy) of plot satisfy equations:

Solution

More from this set:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)

The length ( $x$ ) and breadth ( $y$ ) of plot satisfy equations: