195
Q:

# If each side of a square is increased by 25%, find the percentage change in its area?

 A) 65.25 B) 56.25 C) 65 D) 56

Explanation:

let each side of the square be a , then area = a x a

As given that The side is increased by 25%, then

New side = $\inline \fn_jvn \small \frac{125a}{100}$ = $\inline \fn_jvn \small \frac{5a}{4}$

New area = $\inline \fn_jvn \small \left ( \frac{5a}{4} \right )^{2}$

increased area= $\inline \fn_jvn \small \frac{25a^{2}}{16}-a^{2}$

Increase %= $\inline \fn_jvn \small \frac{\left [ \frac{9a^{2}}{16} \right ]}{a^{2}}x100$ % = 56.25%

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.

10 163
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.

7 158
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%.

7 175
Q:

The difference between circumference and semidiameter of a circle is 37 cm. What is the diameter of the circle ?

 A) 18 cm B) 12 cm C) 16 cm D) 14 cm

Explanation:

circumference of a circle = 2$\inline \small \prod$r

=> 2 × 22/7 × r – r = 37

=> 37/7 × r = 37

=> r = 7 cm.

Diameter D = 2r = 7×2 = 14 cm.

14 225
Q:

The breadth of a rectangular field is 75% of its length. If perimeter of the field is 1050 m, what will be th area of field ?

 A) 65700 sq.m B) 54500 sq.m C) 78700 sq.m D) 67500 sq.m

Explanation:

Let the length be 'l' and breadth be 'b'.

b = l × 3/4__________(a)

2(l+b) = 1050

l+b = 525___________(b)

From equations (a) and (b),

l = 300m, b = 225 m

Area = l × b

= 300 × 225

= 67500 sq.m.