Manjeet wants to donate a rectangular plot of land for a school in his village. When he was 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 m2. 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:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → x − y = 50, 2x + y = 550
The area of the plot is xy. With the length decreased by 50 m and the breadth increased by 50 m, the area is unchanged:
\((x-50)(y+50) = xy\)
\(xy + 50x - 50y - 2500 = xy\)
\(50x - 50y = 2500\)
\(x - y = 50\)
With the length decreased by 10 m and the breadth by 20 m, the area decreases by 5300 m2:
\((x-10)(y-20) = xy - 5300\)
\(xy - 20x - 10y + 200 = xy - 5300\)
\(20x + 10y = 5500\)
\(2x + y = 550\)