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A Learning Portal from Recruitment India

A man walked 20m to cross a rectangular field diagonally if the length of the field is 16cm then the breadth of the field is

A.

11m

B.

12m

C.

13m

D.

14m

Answer with explanation

Answer: Option BExplanation

Let a rectangular field ABCD

A/Q a man cross rectangular field diagonally and he had to walk 20m

So,Diagonal of Rectangle =20m

Length=16m (given)

We know that Each angle of a rectangle is 90°

ADC forms a right angled triangle

AC=16m(perpendicular)

AD=20m(Hypotenus)

CD=?(base)

According to Pythagorean Theorem

h2=b2+p2

(20)2=b2+(16)2

400=b2+256

b2=144

b=√144

b=12m

Workspace

If the area of the trapezium, whose parallel sides are 6 cm and 10 cm is 32 sq. cm, what will be the distance between the parallel sides?

A.

2 cm

B.

4 cm

C.

5 cm

D.

8 cm

Answer with explanation

Answer: Option BExplanation

Parallel sides of a trapezium = 6 cm, and 10 cm

Area of trapezium =1/2 ( sum of the parallel sides ) × distance between the parallel sides

32=1/2 ( 6+10 ) × distance

32=8 × distance

Distance = 32/8 = 4 cm

So, the distance between the parallel lines of trapezium = 4 cm.

Workspace

The ratio of the areas of a square and rhombus whose base is same is:

A.

1:2

B.

2:1

C.

1:1

D.

3:1

Answer with explanation

Answer: Option CExplanation

When parallelogram is on same and located between the same parallels then its area will be equal. It is given rhombus and square are two parallelograms on same base and located between the same parallels.

∴ Area of rhombus = Area of square

∴ Ratio = 1:1

Workspace

The sides of a rectangle are in the ratio 4:3 and its area is 972sq.m find the perimeter of the rectangle?

A.

120m

B.

122m

C.

124m

D.

126m

Answer with explanation

Answer: Option DExplanation

let 4x and 3x be sides of the rectangle

We know that area of rectangle = l×b

4x × 3x = 972

12×2 = 972

X2 = 81

X = 9

Therefore length = 4x = 4×9 = 36m

Breadth = 3x = 3×9 = 27m

Therefore perimeter = 2 (l+b) = 2(36+27) = 126m

Workspace

The ratio between the breadth and perimeter of a rectangle is 2:10. If the area of the rectangle is 428 sq. cm, what is the length of the rectangle?

A.

45.4 cm

B.

25.4 cm

C.

30.4 cm

D.

40.4 cm

Answer with explanation

Answer: Option BExplanation

per the question = 2(L+B)/B = 10/2

2(L+B)/B = 5/1

2L + 2B = 5B

2B – 5B = – 2L

– 3B = – 2L

B = 2/3 L

Given Area = 430 sq. cm.

Area = Length * Breadth

430 = L * 2/3 L

430 = 2/3 L^{2}

Or L^{2} = 1290 / 2

L^{2} = 645

L = 25.4 cm

Workspace

How many cubes of 10cm edge can be put in a cubical box of 1m edge

A.

10

B.

100

C.

1000

D.

10000

Answer with explanation

Answer: Option CExplanation

Number of cubes= (100x100x100) / (10x10x10)= 1000

(OR)

The volume of cubical box =100^3 = 1000000cubic cm

Volume of cubes =10^3 =1000cubic cm

Now, no. Of cubes that can be fit in the cubical box = [(The volume of cubical box)/(volume of 1 cube)]

= 1000000/1000

= 1000 cubes

Workspace

The volume of a wall, 5 times as high as it is broad and 8 times as long as it is high, is 12.8 cu. meters. Find the breadth of the wall.

A.

40cm

B.

30cm

C.

20cm

D.

10cm

Answer with explanation

Answer: Option AExplanation

(or)

Given: The volume of a wall is 12.8 m^{3}.

Height is 5 times the breadth and length is 8 times the height.

Let breadth = x

∴ Height = 5x

⇒ Length = 8 × (5x) = 40x

The volume of a Cuboid is given by l × b × h (here l, b, h are, length, breadth, height respectively)

∴ l × b × h = 12.8

⇒ x × 5x × 40x = 12.8

⇒ 200x^{3} = 12.8

⇒ x^{3} = 12.8/200 m^{3} = 8/125

⇒ x= ∛ (8/125)m = 2/5 m = 0.4 m

∴ x = 0.4m = 0.4 × 100 = 40cm

That is Breadth is: 40cm

Workspace

How many bricks each measuring 25cm x 11.25cm x 6cm, will be needed to build a wall 8m x 6m x 22.5m

A.

5600

B.

600

C.

6400

D.

7200

Answer with explanation

Answer: Option CExplanation

No. of bricks= volume of the wall/volume of 1 brick

= (800 x 600 x 22.5) / (25 x 11.25 x 6) = 6400

Workspace

50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 cu.m , then the rise in the water level in the tank will be:

A.

20 cm

B.

25 cm

C.

35 cm

D.

50 cm

Answer with explanation

Answer: Option BExplanation

Workspace

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