# Areas Quiz Set 007

### Question 1

A rectangular wire 26 × 9 is re-aligned into a rectangle 13 × 27. What is the percentage increase in area?

A

50 %.

B

52 %.

C

48 %.

D

54 %.

Soln.
Ans: a

By inspection, the length has been halved, and breadth tripled. The %-age increase is known through shortcut formulas to be 50%. So the increase is 50%.

### Question 2

What is the ratio of the perimeter of a circle of radius 4 units to that of a square having the circle's diameter as its side?

A

π : 4.

B

π : 2.

C

4 : 3.

D

4 : π.

Soln.
Ans: a

Let X be the radius of the circle, so the side of the square is 2X. The ratio of the perimeters = \${2 × π × X}/{4 × (2X)}\$ = π/4.

### Question 3

The length and breadth of a rectangular area are in the ratio 5 : 3. What is the length of the field if a car travelling at 12 km/h covers one round of the rectangle in 320 minutes?

A

20 km.

B

22 km.

C

18 km.

D

24 km.

Soln.
Ans: a

Let L = 5x and B = 3x. Perimeter = 2 × (5x + 3x) = speed × time = (12 × 320)/60 = 64 km. So x = 4, and L = 5x = 20 km.

### Question 4

The diagonal and one side of a rectangle are 26 m and 24 m. What is the percentage saving of a man who walks along the diagonal instead of the two sides?

A

\$23{9/17}\$%.

B

\$26{1/16}\$%.

C

\$20{3/19}\$%.

D

\$23{14/19}\$%.

Soln.
Ans: a

The side = \$√{26^2 - 24^2}\$ = \$√{676 - 576}\$ = 10. So the saving = (24 + 10) - 26 = 8 meters. So the %-age saving is \$8/34\$ × 100 = \${400/17}\$, which is same as: \$23{9/17}\$%.

### Question 5

What is the smallest number of square tiles that can be laid fully, without cutting, on a floor 36 m by 34 m?

A

306 .

B

307 .

C

305 .

D

308 .

Soln.
Ans: a

The side of the square tile has to be HCF(36, 34) = 2. Hence, the required number is \${36 × 34}/{2 × 2}\$ = 306.