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Q:

The diagonal of the floor of a rectangular closet is 7 $\frac{1}{2}$ feet. The shorter side of the closet is 4 $\frac{1}{2}$ feet. What is the area of the closet in square feet?

A) 9	B) 18
C) 27	D) 36

Answer & Explanation Answer: C) 27

Explanation:

Other side = $\sqrt{d^{2} - s^{2}}$ = $\sqrt{(\frac{225}{4} - \frac{81}{4})}$ = $\sqrt{\frac{144}{4}}$ = 6 ft

Area of closet = (6 x 4.5) sq. ft = 27 sq. ft.

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Q:

A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?

A) 1	B) 2
C) 3	D) 4

Answer & Explanation Answer: C) 3

Explanation:

Area of the park = (60 x 40) = 2400 $m^{2}$

Area of the lawn = 2109 $m^{2}$

Area of the crossroads = (2400 - 2109) = 291 $m^{2}$

Let the width of the road be x metres. Then,

$60 x + 40 x - X^{2} = 291$

$x^{2} - 100 x + 291 = 0$

(x - 97)(x - 3) = 0
x = 3.

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Q:

The percentage increase in the area of a rectangle, if each of its sides is increased by 20%

A) 22%	B) 33%
C) 44%	D) 55%

Answer & Explanation Answer: C) 44%

Explanation:

Let original length = x metres and original breadth = y metres.

Original area = xy sq.m

Increased length = $\frac{120}{100}$ and Increased breadth = $\frac{120}{100}$

New area = $\frac{120}{100} x * \frac{120}{100} y = \frac{36}{25} x y m^{2}$

The difference between the Original area and New area is:

$\frac{36}{25} x y - x y$

$\frac{11}{25} x y$ Increase % = $(\frac{\frac{11}{25} x y}{x y}) * 100$ = 44%

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Q:

The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?

A) 16	B) 18
C) 20	D) 22

Answer & Explanation Answer: B) 18

Explanation:

$\frac{2 (l + b)}{b} = \frac{5}{1}$ => 2l + 2b = 5b => 3b = 2l

b=(2/3)l

Then, Area = 216 cm²

=> l x b = 216 => l x (2/3)l =216

l = 18 cm.

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Q:

An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:

A) 1.04	B) 2.04
C) 3.04	D) 4.04

Answer & Explanation Answer: D) 4.04

Explanation:

100 cm is read as 102 cm.

A1 = (100*100)Sq.cm

A2 = (102*102)Sq.cm

(A2 - A1) = $102^{2} - 100^{2}$ = (102 + 100) x (102 - 100) = 404 sq.cm.

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Q:

The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:

A) 153600	B) 143600
C) 13600	D) 16300

Answer & Explanation Answer: A) 153600

Explanation:

Let length = 3x metres and breadth = 2x metres.

Then, 2(3x + 2x) = 1600 or x = 160.

Length = 480 m and Breadth = 320 m.Area = (480 x 320) sq.m = 153600 sq.m

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Q:

If there are 15 dots on a circle,how many triangles can be formed?

A) 455	B) 450
C) 469	D) 500

Answer & Explanation Answer: A) 455

Explanation:

There are 15 dots in total,and to make a triangle we need to select any three of those dots.

So, $15 C_{3}$ = 455

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Q:

If each of the 8 teams in a league must play each other three times,how many games will be played?

A) 72	B) 84
C) 36	D) 79

Answer & Explanation Answer: B) 84

Explanation:

Since,each member of the league must meet every other member of the league.If they only played each other once,there would be $8 C_{2}$ games.Since,each pairing of teams will occur three times,the answer will be triple.

Therfore, $8 C_{2} * 3$ =84

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