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.
Area of the rectangular plot is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 30,000 sq. m
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:
\((x-50)(y+50) = xy\)
\(50x - 50y - 2500 = 0\)
\(x - y = 50\)
With the length decreased by 10 m and the breadth by 20 m, the area decreases by 5300 m2:
\((x-10)(y-20) = xy - 5300\)
\(-20x - 10y + 200 = -5300\)
\(20x + 10y = 5500\)
\(2x + y = 550\)
Adding the two equations:
\(3x = 600,\quad x = 200\)
\(y = 200 - 50 = 150\)
\(\text{Area} = xy = 200 \times 150 = 30000\ \text{m}^2\)