# Areas Quiz Set 012

### Question 1

The length and breadth of a rectangle are respectively increased by 9% and 1%. What is the % increase in the area?

A

\$10{9/100}\$%.

B

\$11{20/99}\$%.

C

\$8{31/34}\$%.

D

\$12{5/6}\$%.

Soln.
Ans: a

If x% and y% is the increase in the dimensions, then the area of a rectangle increases by \$(x + y + {xy}/100)\$% = \$(9 + 1 + {9 × 1}/100)\$% = \${1009/100}\$, which is same as: \$10{9/100}\$%

### Question 2

A gun is fired towards a circular board consisting of two concentric circles of radii 10 and 4 cm. If each bullet is able to hit the board, what is the probability that it will strike the ring, i.e., the area between the inner and outer circles?

A

\${21/25}\$.

B

\${7/10}\$.

C

1/2.

D

\${21/40}\$.

Soln.
Ans: a

The area of the ring is equal to the difference of the areas of the two circles. π(\$10^2 - 4^2\$) = 84π sq. cm. The total area is π × 102 = 100π. The probability of hitting the ring is \${84π}/{100π}\$ = \${21/25}\$.

### Question 3

A rectangular wire 22 × 3 is re-aligned into a rectangle 11 × 9. 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 4

The length of a square is increased by 4%, what is the % increase in area?

A

8.16%.

B

17%.

C

11%.

D

16.32%.

Soln.
Ans: a

If x% is the increase in length, then area increases by \$(2x + x^2/100)\$%. Putting x = 4, the increase is \$(2 × 4 + 4^2/100)\$% = 8.16%

### Question 5

Three squares have their sides such that they are in an AP(Arithmetic Progression). If the side of the middle square is 19, what is the area of the square whose side is equal to the sum of the sides of these three squares?

A

3249 sq. units.

B

3253 sq. units.

C

3245 sq. units.

D

3257 sq. units.

Soln.
Ans: a

Let the sides of the three squares be 19 - d, 19 and 19 + d, where d is the common difference. The sum of these is 57, and the area would be \$57^2\$ = 3249 sq. units. This Blog Post/Article "Areas Quiz Set 012" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2020-02-07. Published on: 2016-05-09