Q8 of 40 Page 86

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

Let the length be x and breadth be y

According to question,


xy-80 = (x-5)(x + 2)


⇒xy-80 = xy + 2x-5y-10


⇒-80 + 10 = 2x-5y


⇒ 2x-5y = -70 ….I


(x + 10)(y-5) = xy + 50


⇒ xy-5x + 10y-50 = xy + 50


⇒ -5x + 10y = 100


⇒ -x + 2y = 20 ….II


Multiplying Eq. II by 2


2x-5y = -70


-2x + 4y = 40


-y = -30


y = 30


substituting y = 30 in eq. II


-x + 2× 30 = 20


-x = 20-60


x = 40


length = 40units and breadth = 30 units


More from this chapter

All 40 →
6

Half the perimeter of a rectangular garden is 36 m. If the length is 4m more than its width, is 36 m. Find the dimensions of the garden.

 7

We have a linear equation 2x + 3y-8 = 0. Write another linear equation in two variables such that the geometrical representation of the pair so formed is intersecting lines.

Now, write two more linear equations so that one forms a pair of parallel lines and the second forms coincident line with the given equation.

 9

In X class, if three students sit on each bench, one student will be left. If four students sit on each bench, one bench will be left. Find the number of students and the number of benches in that class.

 1

The ratio of incomes of two persons is 9 : 7 and the ratio of their expenditures is 4 : 3. If each of them manages to save D2000 per month, find their monthly income.