67
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%

Explanation:

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:

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

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.

7 169
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

Explanation:

Area =    = 96

Sum of Area =

3 81
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

Explanation:

3 88
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

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.

13 308
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

Explanation:

Let the side of the square be 's' cm

length of rectangle = (s+5) 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

21 632
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

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.

21 659
Q:

The question given below contain two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question ?

Question :

What is the height of a right-angled triangle ?

Statements :

A. The area of the triangle is 20 times its base.

B. The perimeter of the triangle is equal to that of a square of the side 10 cm.

 A) Only statement A is required B) Only statement B is required C) Both A & B are required D) Neither (A) nor (B) is reuired

Explanation:

From statement (A),

20b = (1/2) × b × h

h = 40 cm.

20 532
Q:

The length, breadth and height of a room are in the ratio 7:3:1. If the breadth and height are doubled while the length is halved, then by what percent the total area of the 4 walls of the room will be increased  ?

 A) 90% B) 88% C) 85% D) 84%

Explanation:

Let length, breadth and height of the room be 7, 3, 1 unit respectively.

Area of walls = 2(l+b)xh = 2(7+3)x1 = 20 sq. unit.

Now, length, breadth and height of room will become 3.5, 6 and 2 respectively.

Area of walls = 2(l+b)xh = 2(3.5+6)x2 = 38 sq. unit.

% Increase in the area of walls = (38-20)x100/20 = 90%.