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The area of a rectangle gets reduced by 80 sq. units if its length is reduced by 5 units and the breadth is increased by 2 units. If we increase the length by 10 units and decrease the by 5 units, the area is increased by 50 sq. units. Find the length and breadth of the rectangle.

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40 and 30 units

20 and 30 units

35 and 45 units

32 and 30 units

answer is A.

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Detailed Solution

Area of Rectangle (A) = length (l) \times breadth (b)

A = lb \to eq (1)

According to question,

A - 80 = (l - 5) (b + 2) \to eq (2)

A + 50 = (l + 10) (b - 5) \to eq (3)

From eq (1) and (2)

lb - 80 = lb + 2 l - 5 b - 10

5 b - 2 l = 70 \to eq (4)

From eq (1) and (3)

lb + 50 = lb - 5 l + 10 b - 50

5 l - 10 b = - 100

2 b - l = 20

l = 2 (b - 10) \to eq (5)

From eq (4) and (5)

5 b - 2 (2 (b - 10)) = 70

5 b - 4 b + 40 = 70

b = 30 units

and, l = 2 (30 - 10)

l = 40 units

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