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The area of a rectangle gets reduced by $9$ sq. units, if its length is reduced by $5$ units and the breadth, is increased by $3$ units. If we increase the length by $3$ units and breadth by $2$ units, the area is increased by $67$ sq. units. Find the length and breadth of the rectangle.

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length

= 12

units, breadth

= 6

units

length

= 20

units, breadth

= 15

units

length

= 17

units, breadth

= 9

units

length

= 21

units, breadth

= 8

units

answer is C.

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Detailed Solution

Given a rectangle.
Let the length and breadth of the rectangle be

x

and

y

∴

Area of rectangle

= xy

According to given condition:

(x - 5) (y + 3) = xy - 9

∴ xy + 3 x - 5 y - 15 = xy - 9

\Rightarrow 3 x - 5 y = 6

.........(1)
And,

(x + 3) (y + 2) = xy + 67

∴ xy + 2 x + 3 y + 6 = xy + 67

\Rightarrow 2 x + 3 y = 61

...........(2)
On multiplying equation (1) by

2

, we get,

6 x - 10 y = 12

..........(3)
On multiplying equation (2) by

3

, we get,

6 x + 9 y = 183

.....(4)
On subtracting (4) from (3), we get,

- 19 y = - 171

\Rightarrow y = 9

by putting

y = 9

in (1), we get,

3 x - 5 (9) = 6

\Rightarrow x = 17

∴

Length

= 17

units and breadth

= 9

units.
Therefore, option (3) is correct.

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The area of a rectangle gets reduced by 9 sq. units, if its length is reduced by 5 units and the breadth, is increased by 3 units. If we increase the length by 3 units and breadth by 2 units, the area is increased by 67 sq. units. Find the length and breadth of the rectangle.

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The area of a rectangle gets reduced by $9$ sq. units, if its length is reduced by $5$ units and the breadth, is increased by $3$ units. If we increase the length by $3$ units and breadth by $2$ units, the area is increased by $67$ sq. units. Find the length and breadth of the rectangle.