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Q:

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

A) 56.25%	B) 36.25%
C) 16.25%	D) 12.25%

Answer & Explanation Answer: A) 56.25%

Explanation:

Let each side of the square be a. Then, area = . $a^{2}$
New side = $\frac{125 a}{100} = \frac{5 a}{4}$ . New area = ${(\frac{5 a}{4})}^{2}$ = $(\frac{25 a^{2}}{16})$

Increase in area = $\frac{25 a^{2}}{16} - a^{2} = \frac{9 a^{2}}{16}$
Increase% = $[\frac{9 a^{2}}{16} * \frac{1}{a^{2}} * 100]$ % = 56.25%.

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Q:

The diagonals of two squares are in the ratio of 2 : 5. Find the ratio of their areas.

A) 4:25	B) 3:25
C) 3:15	D) 5:25

Answer & Explanation Answer: A) 4:25

Explanation:

Let the diagonals of the squares be 2x and 5x respectively.
Ratio of their areas = $\frac{1}{2} * {(2 x)}^{2} : \frac{1}{2} * {(5 x)}^{2} = 4 : 25$

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Q:

A tank is 25 m long, 12 m wide and 6 m deep. The cost of plastering its walls and bottom at 75 paise per sq. m, is:

A) rs.458	B) rs,558
C) rs.658	D) rs.758

Answer & Explanation Answer: B) rs,558

Explanation:

Area to be plastered= [2(l + b) x h] + (l x b)

= [2(25 + 12) x 6] + (25 x 12)

= (444 + 300)

= 744 sq.m

Cost of plastering = Rs.744 x (75/100)

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Q:

The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ 26.50 per metre is Rs. 5300, what is the length of the plot in metres?

A) 40	B) 20
C) 30	D) none of these

Answer & Explanation Answer: D) none of these

Explanation:

Let breadth = x metres.
Then, length = (x + 20) metres.

Perimeter =5300/23.50

2[(x + 20) + x] = 200
2x + 20 = 100
2x = 80
x = 40.
Hence, length = x + 20 = 60 m.

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Q:

What is the least number of squares tiles required to pave the floor of a room 15.17 m long and 9.02 m broad?

A) 814	B) 714
C) 614	D) 713

Answer & Explanation Answer: A) 814

Explanation:

Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm.

Area of each tile = $(41 \times 41) c m^{2}$

Required number of tiles = $\frac{1517 \times 902}{41 \times 41}$ = 814

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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:

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:

A research team of 6 people is to be formed from 10 chemists,5 politicians, 8 economists and 15 biologists.How many teams have atleast 5 chemists?

A) 7350	B) 6400
C) 6379	D) 7266

Answer & Explanation Answer: D) 7266

Explanation:

$10 C_{5} * 28 C_{1} * 10 C_{6} = 7266$

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