Exercise : 1


1. The area of rectangular field is 460 square metres. If the length is 15 per cent more than the breadth ,what is the breadth of the rectangular field?
(a) 15 metres
(b) 26 metres
(c) 34.5 metres
(d) Cannot be determined
(e) None of these
Ans.e

Let the breadth of the rectangular field be ‘x’ m. Then,length of the field will be

\(x + \frac{x \times 15}{100} = \frac{23x}{20}\)

Now, \(x \times \frac{23x}{20} = 460\)

or, 23x2 = 460 × 20

or, x2 = 20 × 20

or, x = 20 m

2. What will be the cost of gardening 1-metre – broad boundary around a rectangular plot having perimeter of 340 metres at the rate of 10 per square metre?
(a) 3400
(b) 1700
(c) 3440
(d) Cannot be determined
(e) None of these
Ans.c

Let l and b be the length and breadth of rectangular plot respectively.

∴ According to the question,we have

2(l + b) = 340 ⇒ l + b = 170

Now, (l + 2) and (b + 2) be the length and breadth of plot with boundary.

∴ Required area = (l + 2) (b + 2) – lb

= lb + 2l + 2b + 4 – lb

= 2(l + b) + 4 = 344

∴ Required cost = 344 × 10 = 3440

3. The cost of paint is 60 per kilograme. A kilogram paint covers 20 square feet. How much will it cost to paint the outside of a cube having each side 10 feet?
(a) 3000
(b) 900
(c) 1800
(d) 360
(e) None of these
Ans.c

Area of cube

= 6× (side)2 = 6 × 10 × 10 = 600 square feet.

Cost to paint outside of the cube = 60020 × 60

= 1800

4. 20 buckets of water fill a tank when the capacity of each bucket is 13.5 litres. How many buckets will be required to fill the same tank if the capacity of each bucket is 9 litres?
(a) 30
(b) 32
(c) 60
(d) Data inadequate
(e) None of these
Ans.a

Capacity of the tank = 20 × 13.5= 270 litres

When the capacity of each bucket = 9 litres, then the required no. of buckets

= 2709 = 30

5. The breadth of a rectangular hall is two-thirds of its length. If the area of the hall is 2400 sq metres, what is the length in metres?
(a) 120
(b) 80
(c) 60
(d) 40
(e) None of these
Ans.c

Let the length of the rectangular hall be ‘x’ m, then the breadth of the rectangular hall = 2x3 m.

Area of hall = 2x3 × x = 2x23

or, 2x23 = 2400 or x = 60 m

6. If a pair of opposite sides of a square is increased by 5cm each, then the ratio of the sides of the new figure is 3 : 2. What is the original area of the square?
(a) 125 cm2
(b) 225 cm2
(c) 81 cm2
(d) 100 cm2
(e) None of these
Ans.d

Let the original side of the square = x cm

\(\frac{x + 5}{x} = \frac{3}{2}\) or 2x + 10 = 3x

\ x = 10 cm

\ original area = (10)2 = 100 cm2

7. An equilateral triangle, a square and a circle have equal perimeters. If T denotes the area of the triangle, S, the area of the square and C, the area of the circle, then :
(a) S > T > C
(b) T > C > S
(c) T > S > C
(d) C > S > T
(e) None of these
Ans.d

Let the perimeter of each be a.

Then, side of the equilateral triangle = a3; side of square = a4; radius of the circle = a.

\(T = \frac{\sqrt{3}}{4} \times \left(\frac{a}{2} \right)^{2} = \frac{\sqrt{3}a^{2}}{36}\); S = (a4)2 = a216;

C = π × (a)2 = a2 = 7a288

So, C > S > T.

8. The capacity of a cylindrical tank is 246.4 litres. If the height is 4 metres, what is the diameter of the base?
(a) 1.4 metres
(b) 2.8 metres
(c) 28 metres
(d) 14 metres
(e) none of these
Ans.e

Capacity (volume) of a cylindrical tank = πr2h

(Here r = radius and h = height of the tank)

Now, from the question, 246.4 × 0.001 = 227 × r2 × 4

[∵ 1 litre = 1000 cm3 = 0.001 m3]

or, \(\frac{0.2464 \times 7}{22 \times 4}\) = r2

or,r = 0.14 m

or,diameter = 2r = 0.28 m

9. The length of one pair of opposite sides of a square is increased by 5 cm on each side the ratio of the length and the breadth of the newly formed rectangle becomes 3 : 2. What is the area of the original square?
(a) 25 sq.cm
(b) 81 sq.cm
(c) 120 sq.cm
(d) 225 sq.cm
(e) None of these
Ans.e

Let original length of each side = x cm.

Then, its area = (x2)cm2.

Length of rectangle formed = (x + 5) cm

and its breadth = x cm.

\(\frac{x + 5}{x} = \frac{3}{2}\) ⇔ 2x + 10 = 3x ⇔ x = 10

∴ Original length of each side = 10 cm and its area = 100 cm2

10. The length and the breadth of a rectangle are in the ratio of 3 : 2 respectively. If the sides of the rectangle are extended on each side by 1 metre, the ratio of length to breadth becomes 10 : 7. Find the area of the original rectangle in square metres.
(a) 256
(b) 150
(c) 280
(d) Data inadequate
(e) None of these
Ans.e

Let the length and breadth be l and b respectively.

lb = 32 or l = 32b .....(i)

\(\frac{l + 1}{b + 1} = \frac{10}{7}\) or 7l - 10b = 3 .....(ii)

From eq. (i)

10.5b – l 0b = 6 or, 0.5b = 3 or, b = 6 and l = 9

Area = l × b = 6 × 9 = 54 m2