| Directions: (1 - 5) |
| Manjit 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 cm and breadth is increased by 50 m, then its area will remain same, but if length is decreased by 10 m and breadth is decreased by 20 m, then its area will decrease by \[5300\text{ }{{m}^{2}}\]. |
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| Based on the information given above, answer the following questions : |
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.
Correct Answer: B
Solution :
Area \[=xy\], length \[=x-50\], Breadth \[=y+50\] \[\therefore \,\] Area of rectangle \[=\left( x-50 \right)\,\left( y+50 \right)\] \[=xy+50x-50y-2500\] \[\Rightarrow \,\,\,xy=xy+50x-50y-2500\] \[\Rightarrow \,\,x-y\,\,=50\] (1) Also New length \[=x-10\], New breadth \[=y-20\] \[\therefore \,\,Area=\left( x-10 \right)\left( y-20 \right)\] A.T.Q. \[xy-5300=\left( x-10 \right)\left( y-20 \right)\] \[\Rightarrow \,\,xy-5300=xy-20x-10y+200\] \[\Rightarrow \,\,2x+y=550\]
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