Manjit wants to donate a rectangle plot of level for a school in his v

1.	Manjit wants to donate a rectangle plot of level 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 50m and breadth is increased by 50m, then its area will remain same, but if length increased by 10 m and breadth is decreased by 20m, then its area will decrease by 5300 m2.with the help of above facts, answer the following question:The relation between x and y is given by :(a) x − y = 50, 2x − y = 550(b) x − y = 50, 2x + y = 550(c) x + y = 50, 2x + y = 550(d) x + y = 50, 2x − y = 550.
Answer» Let the length of plot is x m, the breadth of the plot is y m. Therefore, the area of the plot is xy m². According to the first condition, length is decreased by 50 m and breadth is increased by 50 m then the area remains same. Therefore, (x − 50)(y + 50) = xy ⇒ xy + 50x − 50y − 2500 = xy ⇒ 50x − 50y = 2500 ⇒ x − y = 50. ... (1) According to the second condition, length is decreased by 10 m and breadth is decreased by 20 m then the area is decreased by 5300 m² . Therefore, (x − 10)(y − 20) = xy − 5300 ⇒ xy − 20x − 10y + 200 = xy − 5300 ⇒ −20 x − 10y = −5500 ⇒ 2x + y = 550. ... (2) Hence, option (b) is correct.

Manjit wants to donate a rectangle plot of level 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 50m and breadth is increased by 50m, then its area will remain same, but if length increased by 10 m and breadth is decreased by 20m, then its area will decrease by 5300 m2.with the help of above facts, answer the following question:The relation between x and y is given by :(a) x − y = 50, 2x − y = 550(b) x − y = 50, 2x + y = 550(c) x + y = 50, 2x + y = 550(d) x + y = 50, 2x − y = 550.

Answer»

Let the length of plot is x m, the breadth of the plot is y m.

Therefore, the area of the plot is xy m².

According to the first condition, length is decreased by 50 m and breadth is increased by 50 m then the area remains same.

Therefore, (x − 50)(y + 50) = xy ⇒ xy + 50x − 50y − 2500 = xy ⇒ 50x − 50y = 2500

⇒ x − y = 50. ... (1)

According to the second condition, length is decreased by 10 m and breadth is decreased by 20 m then the area is decreased by 5300 m² .

Therefore, (x − 10)(y − 20) = xy − 5300

⇒ xy − 20x − 10y + 200 = xy − 5300

⇒ −20 x − 10y = −5500

⇒ 2x + y = 550. ... (2)

Hence, option (b) is correct.