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A Learning Portal from Recruitment India

A cistern 6 m long and 4 m wide contains water up to a breadth of 1 m 25 cm. Find the total area of the wet surface

A.

49 m sqaure

B.

42 m sqaure

C.

64 m sqaure

D.

52 m sqaure

Answer with explanation

Answer: Option AExplanation

Explanation:

Area of the wet surface =

2[lb+bh+hl] – lb = 2 [bh+hl] + lb

= 2[(4*1.25+6*1.25)]+6*4 = 49 m square

Workspace

Dean has a cardboard box whose length, breadth and height are in the ratio 1:2:3. He makes a new box such that the length, breadth and height got increased by 100%, 200% and 200% respectively. How much less is volume of old box than the new box

A.

16 times less

B.

17 times less

C.

12 times less

D.

24 times less

Answer with explanation

Answer: Option BExplanation

Workspace

Water flows out through a circular pipe whose internal diameter is 2 cm, at the rate of 6 metres per second into a cylindrical tank, the radius of whose base is 60 cm. By how much will the level of water rise in 30 minutes ?

A.

A.

B.

C.

D.

Answer with explanation

Answer: Option BExplanation

Workspace

A.

121 : 125

B.

125 : 121

C.

15 : 11

D.

11: 15

Answer with explanation

Answer: Option AExplanation

Workspace

The length of a rectangle is 12 m more than the side of the square and the breadth of the rectangle is 5 m less than the side of the square. If the area of the square is 784 Sq m. what is the area of the rectangle?

A.

920 Sq m

B.

660 Sq m

C.

780 Sq m

D.

840 Sq m

Answer with explanation

Answer: Option AExplanation

Area of square = 784 Sq m

Side of the square = 28 m

Length of the rectangle = 28 + 12 = 40 m

Breadth of the rectangle = 28 – 5 = 23 m

Area of the rectangle = 40*23 = 920 Sq m

Workspace

A solid cylinder of radius r and height h is placed over other cylinder of same height and radius. The total surface area of the shape so formed is?

A.

4πrh + 4πr^{2}

B.

4πrh − 4πr^{2}

C.

4πrh + 2πr^{2}

D.

4πrh − 2πr^{2}

Answer with explanation

Answer: Option CExplanation

Since the total surface area of cylinder of radius r and height h = 2πrh + 2πr^{2}.

When one cylinder is placed over the other cylinder of same height and radius,

Then height of new cylinder = 2h

And radius of the new cylinder = r

Therefore total surface area of new cylinder

= 2πr (2h) + 2πr^{2}

= 4πrh + 2πr^{2}

Workspace

The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?

A.

16cm

B.

24cm

C.

18cm

D.

Data inadequate

Answer with explanation

Answer: Option CExplanation

2(l+b)/b = 5/1

=> 2l + 2b = 5b

=> 3b = 2l

=> b =(2/3) x l

Then, Area = 216 sq.cm

l x b = 216

=> l x [(2/3)x l] =216

=> l x l = 324

=> l = 18 cm.

Workspace

A hollow cube of internal edge 22cm is filled with spherical marbles of diameter 0.5 cm and it is assumed that 1/8th space of the cube remains unfilled. Then the number of marbles that the cube can accommodate is?

A.

142244

B.

142396

C.

142496

D.

142596

Answer with explanation

Answer: Option AExplanation

Workspace

A cuboid of dimension 24cm x 9cm x 8 cm is melted and smaller cubers are of side 3 cm is formed.find how many such cubes can be formed?

A.

56

B.

64

C.

48

D.

40

Answer with explanation

Answer: Option BExplanation

Volume of cuboid = (24 x 9 x 8) cm = 1728 cu.cm

Volume of small cube = (3 x 3 x 3) cm = 27 cu.cm

So, No. of small cubes formed = 1728/27 = 64.

Workspace

A rectangular courtyard, the sides of which are in the ratio of 4:3, cost Rs.600 for paving at 50 p per m^{2}; find the length of the diagonal of the courtyard?

A.

25 m

B.

35 m

C.

45 m

D.

50 m

Answer with explanation

Answer: Option DExplanation

1 m^{2} —- 1/2

? —– 600 => 1200 m^{2}

4x * 3x = 1200 => x = 10

Workspace

The biggest possible circle is inscribed in rectangle of length 10 m and breadth 7 m. Then the area of circle is?

A.

35.8 m^{2}

B.

36.5 m^{2}

C.

30.5 m^{2}

D.

38.5 m^{2}

Answer with explanation

Answer: Option DExplanation

Radius = Breadth /2 = 7/2 = 3.5

Area = 22*3.5*3.5/7 = 269.5/7 = 38.5 m^{2}

Workspace

The circumference of a circle is half of the perimeter of a rectangle. The area of the circle is 2464 sq. m. What is the area of the rectangle if the breadth of the rectangle is 80 m?

A.

7054 Sq m

B.

6128 Sq m

C.

7680 Sq m

D.

5572 Sq m

Answer with explanation

Answer: Option CExplanation

Area of a circle= πr^{2}

2464 = 22r^{2}/7

2464*(7/22) = r^{2}

r^{2 }= 784

r = 28 m

Circumference = 2*22/7 * 28 = 176 sq. m

Perimeter of the rectangle = 2*176 = 352 sq. m

352 = 2(l + 80)

176 = l + 80

l = 176 – 80

l = 96

Area of the rectangle = 96*80 = 7680 sq. m

Workspace

A horse is tethered to a peg with a 16 cm long rope at the corner of a 31 cm long and 27cm wide rectangular grass field. What area of the field will the horse graze?

A.

201.1 cm^{2}

B.

251.6 cm^{2}

C.

111.2 cm^{2}

D.

245.3 cm^{2}

Answer with explanation

Answer: Option AExplanation

Area = [22*16*16/7] / 4

= 5632/7*4 = 201.1 cm^{2}

Workspace

If the breadth of a parallelogram is increased by 30% while the height of the parallelogram is decreased by 20% then find percentage change in area of the parallelogram?

A.

8 % increased

B.

5 % decreased

C.

4 % increased

D.

9 % decreased

Answer with explanation

Answer: Option CExplanation

Let the breadth and height of the parallelogram is 10 cm and 10cm,

Normal area= 10*10= 100

New length= 10*130/100= 13

New height= 10*80/100= 8

New area= 13*8= 104

Required percentage = [(104 – 100)/100]*100 = 4 % increased

Workspace

A.

10cm

B.

9cm

C.

12cm

D.

15cm

Answer with explanation

Answer: Option DExplanation

Side of 1^{st} square = 60/4 = 15 cm.

Smallest side of right angled triangle= 15 −6 = 9 cm.

Length of 2^{nd} rectangle = 80/5 = 16 cm.

Second largest side of the 1strectangle = 16−4 = 12 cm.

Largest side = hypotenuse=√9^2+12^2=15cm

Workspace

The side of the equilateral triangle is equal to the diameter of the circle. The area of the equilateral triangle is 196√3 Sq cm. Find the circumference of the circle?

A.

74 cm

B.

88 cm

C.

66 cm

D.

92 cm

Answer with explanation

Answer: Option BExplanation

The area of the equilateral triangle = 196√3 Sq cm

The area of the equilateral triangle = (√3/4)*a^{2}

(√3/4)*a^{2} = 196√3

a^{2 }= 196*4

Side (a) = 14*2 = 28 cm

The diameter of the circle = 28 cm

Radius (r) = 14 cm

Circumference of the circle = 2πr = 2*(22/7)*14 = 88 cm

Workspace

After measuring 320m of a rope, it was discovered that the measuring metre rod was 6cm longer. The true length of the rope measured is

A.

230m 860cm

B.

320m 60cm

C.

329m 60cm

D.

320m 860cm

Answer with explanation

Answer: Option CExplanation

True length= 320m + 320* 3cm

320m + 960cm

329m 60cm(1m=100cm)

Workspace

How many marbles of 10cm length and 7cm width are required to pave the floor of room 7m length and 4m breadth?

A.

3200

B.

2800

C.

4000

D.

5100

Answer with explanation

Answer: Option CExplanation

Area of floor = 700*400 = 280000

Area of marble = 10*7 = 70

N = 280000/70 = 4000

Workspace

Two roads each 10m wide has been made running perpendicularly to each other inside a rectangular field of dimension 90m X 50m. What is the cost of spreading pebbles over them at the rate of Rs.8 per m².?

A.

10400

B.

15400

C.

17500

D.

20600

Answer with explanation

Answer: Option AExplanation

Area of Roads = (l + b – w) * w

Area of Roads = (90 + 50 – 10) * 10 = 1300m²

Cost = 1300 * 8 = 10400

Workspace

In a rectangle the ratio of the length and breadth is 3:2. If each of the length and breadth is increased by 3m their ratio becomes 10:7. The area of the original rectangle in m² is?

A.

384

B.

486

C.

346

D.

476

Answer with explanation

Answer: Option BExplanation

[3x + 3 / 2x + 3] = 10/ 7

x = 9

Area of the original rectangle = 3x * 2x = 6x²

Area of the original rectangle = 6 * 81 = 486m²

Workspace

Inside a square plot a circular garden is developed which exactly fits in the square plot and the diameter of the garden is equal to the side of the square plot which is 14m. What is the area of space left out in the square plot after developing the garden?

A.

32m^{2}

B.

40m^{2}

C.

35m^{2}

D.

42m^{2}

Answer with explanation

Answer: Option DExplanation

area of space left = 14*14 – (3.14*7*7)

= 196 – 153.86

= 42.14 = 42 m^{2}

Workspace

The height of a cone is 60cm. A small cone is cut off at the top of by a plane parallel to its base. If its volume is 1/64 of volume of the cone, at what height above the base is the section made?

A.

23cm

B.

15cm

C.

20cm

D.

17cm

Answer with explanation

Answer: Option BExplanation

(⅓ * π * r1^2 * h1 )/ (⅓ π * r^2 * h) / 1/64

(r1/r)^2 * h1/h = 1/64

(h1/h) ^3 = (¼)^3 ( r1/r = h1/h)

h1 = ¼ * 60=15

Workspace

**A circular path runs round a circular garden. If the difference between the circumference of the outer circle and inner circle is 88m. Find the width of Path?**

A.

14 m

B.

17 m

C.

16 m

D.

15 m

Answer with explanation

Answer: Option AExplanation

Width of the Road = R – r

2πR – 2πr = 88

R – r = 14 m

Workspace

A.

35

B.

21

C.

14

D.

20

Answer with explanation

Answer: Option CExplanation

Workspace

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