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Q:

# If the radius of a circle is decreased by 50%, find the percentage decrease in its area.

 A) 55% B) 65% C) 75% D) 85%

Answer:   C) 75%

Explanation:

Let original radius = R.

New radius = $\frac{50}{100}R$$\frac{50}{100}R$

Original area =$\frac{R}{2}$  and new area = ${\mathrm{\pi R}}^{2}$

$\frac{3{\mathrm{\pi R}}^{2}}{4}*\frac{1}{{\mathrm{\pi R}}^{2}}*100$

Decrease in area = $\mathrm{\pi }{\left(\frac{\mathrm{R}}{2}\right)}^{2}=\frac{{\mathrm{\pi R}}^{2}}{4}$ = 75%

Q:

Square units 13 by 9 of an office area is

 A) 97 B) 117 C) 107 D) 127

Answer & Explanation Answer: B) 117

Explanation:

Square units 13 by 9 of an office means office of length 13 units and breadth 9 units.

Now its area is 13x 9 = 117 square units or units square.

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2 332
Q:

Find the area of the square whose side is equal to the diagonal of a rectangle of length 3 cm and breadth 4 cm.

 A) 25 sq.cm B) 16 sq.cm C) 9 sq.cm D) 4 sq.cm

Answer & Explanation Answer: A) 25 sq.cm

Explanation:

Given length of the rectangle = 3 cm

Breadth of the rectangle = 4 cm

Then, the diagonal of the rectangle

Then, it implies side of square = 5 cm

We know that Area of square = S x S = 5 x 5 = 25 sq.cm.

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7 528
Q:

The length of a class room floor exceeds its breadth by 25 m. The area of the floor remains unchanged when the length is decreased by 10 m but the breadth is increased by 8 m. The area of the floor is

 A) 5100 sq.m B) 4870 sq.m C) 4987 sq.m D) 4442 sq.m

Answer & Explanation Answer: A) 5100 sq.m

Explanation:

Let the breadth of floor be 'b' m.

Then, length of the floor is 'l = (b + 25)'

Area of the rectangular floor = l x b = (b + 25) × b

According to the question,

(b + 15) (b + 8) = (b + 25) × b

2b = 120

b = 60 m.

l = b + 25 = 60 + 25 = 85 m.

Area of the floor = 85 × 60 = 5100 sq.m.

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23 1723
Q:

The sides of a right-angled triangle are 12 cm, 16 cm, 20 cm respectively. A new right angle Δ is made by joining the midpoints of all the sides. This process continues for infinite then calculate the sum of the areas of all the triangles so made.

 A) 312 sq.cm B) 128 sq.cm C) 412 sq.cm D) 246 sq.cm

Answer & Explanation Answer: B) 128 sq.cm

Explanation:

Area =    = 96

Sum of Area =

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13 1338
Q:

A room is 15 feet long and 12 feet broad. A mat has to be placed on the floor of the room leaving 1.5 feet space from the walls. What will be the cost of the mat at the rate of Rs. 3.50 per squire feet?

 A) 378 B) 472.5 C) 496 D) 630

Answer & Explanation Answer: A) 378

Explanation:

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15 1095
Q:

A circular piece of thin wire is converted into a rhombus of side 11 cm. Find the diameter of the circular piece?

 A) 28 cm B) 3.5 cm C) 7 cm D) 14 cm

Answer & Explanation Answer: D) 14 cm

Explanation:

Circular piece is 4 x 11 = 44 cm long,

Then Circumference of circle is given by,

44 = pi x D, where D is the diameter

D = 44 / pi

Take pi = 22 / 7, then

D = 44 / (22/7) = (44 x 7) / 22

D = 14 cm.

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15 1236
Q:

The area of a square is equal to the area of a rectangle. The length of the rectangle is 5 cm more than a side of the square and its breadth is 3 cm less than the side of the square. What is the perimeter of the rectangle ?

 A) 15 cm B) 18 cm C) 34 cm D) 26 cm

Answer & Explanation Answer: C) 34 cm

Explanation:

Let the side of the square be 's' cm

length of rectangle = (s+5) cm

breadth of rectangle = (s-3)cm

(s+5) (s-3) =

${s}^{2}$ - 5s - 3s - 15 = ${s}^{2}$

2s = 15

Perimeter of rectangle = 2(L+B) = 2(s+5 + s–3) = 2(2s + 2)

= 2(15 + 2) = 34 cm

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25 1379
Q:

Area of a square and a rectangle are equal. If side of the square is 40 cm and length of the rectangle is 64 cm, what is the perimeter of the rectangle ?

 A) 187 cm B) 178 cm C) 149 cm D) 194 cm

Answer & Explanation Answer: B) 178 cm

Explanation:

Area of square = 40 x 40

= 1600 sq.cm

Given that the areas of Square and Rectangle are equal

=> Area of rectangle = 1600 Sq.cm

We know that, Area of rectangle = L x B

Given L = 64 cm

Breadth of rectangle = 1600/64 = 25 cm

Perimeter of the rectangle = 2(L + B) = 2(64+25) = 178 cm.

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