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Q:

If the radius of a circle is decreased by 50% , find the percentage decrease in its area.

A) 75%	B) 65%
C) 35%	D) 25%

Answer & Explanation Answer: A) 75%

Explanation:

let original radius = r and new radius = (50/100) r = r/2

original area = ${πr}^{2}$ and new area = $π {(r / 2)}^{2}$

decrease in area = $3 {πr}^{2} / 4$ * $\frac{1}{{πr}^{2}}$ *100 = 75%

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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

Answer & Explanation Answer: B) 56.25

Explanation:

let each side of the square be a , then area = $a^{2}$

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

New side = 125a/100 = 5a/4

New area = ${(\frac{5 a}{4})}^{2}$

Increased area= $\frac{25 a^{2}}{16} - a^{2}$

Increase %= $\frac{[9 a^{2} / 16]}{a^{2}} * 100$ % = 56.25%

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Q:

A tea expert claims that he can easily find out whether milk or tea leaves were added first to water just by tasting the cup of tea. In order to check this claims 10 cups of tea are prepared, 5 in one way and 5 in other. Find the different possible ways of presenting these 10 cups to the expert.

A) 340	B) 210
C) 290	D) 252

Answer & Explanation Answer: D) 252

Explanation:

Since there are 5 cups of each kind,prepared with milk or tea leaves added first,are identical hence,total number of different people ways of presenting the cups to the expert is 10!/(5! x 5!)= 252

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Q:

In measuring the sides of a rectangle, one side is taken 5% in excess and the other 4% in deficit. Find the error percent in the area, calculate from the those measurements.

A) .7%	B) 0.8%
C) 0.9%	D) 0.3%

Answer & Explanation Answer: B) 0.8%

Explanation:

let x and y be the sides of the rectangle then

correct area = $\frac{105}{100} x \times \frac{96}{100} y$

Error% = $\frac{504}{500} x y - x y = \frac{4}{500} x y$ %

$\frac{4}{500} x y \times \frac{1}{x y} \times 100 = \frac{4}{5} = 0.8$

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Q:

The length of a rectangle is twice its breadth if its length is decreased by 5cm and breadth is increased by 5cm, the area of the rectangle is increased by 75 sq cm. Find the length of the rectangle.

A) 30	B) 40
C) 50	D) 60

Answer & Explanation Answer: B) 40

Explanation:

let length = 2x and breadth = x then
(2x-5) (x+5) = (2x * x)+75
5x-25 = 75 => x=20
length of the rectangle = 40 cm

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Q:

A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and the other only 4. In how many ways can they travel?

A) 126	B) 120
C) 146	D) 156

Answer & Explanation Answer: A) 126

Explanation:

There are 8 students and the maximum capacity of the cars together is 9.

We may divide the 8 students as follows

Case I: 5 students in the first car and 3 in the second
Case II: 4 students in the first car and 4 in the second

Hence, in Case I: 8 students are divided into groups of 5 and 3 in8C3 ways.

Similarly, in Case II: 8 students are divided into two groups of 4 and 4 in 8C4ways.

Therefore, the total number of ways in which 8 students can travel is:
$8 C_{3} + 8 C_{4}$ =56 + 70= 126

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Q:

One side of a rectangular field is 15m and one of its diagonal is 17m. Find the area of field?

A) 110	B) 120
C) 130	D) 140

Answer & Explanation Answer: B) 120

Explanation:

Other side = [(17 x 17) - (15 x 15)] = (289 - 225) = 8m
Area = 15 x 8 =120 sq. m

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Q:

If the radius of a circle is decreased by 50%, find the percentage decrease in its area.

A) 55%	B) 65%
C) 75%	D) 85%

Answer & Explanation Answer: C) 75%

Explanation:

Let original radius = R.

New radius = $\frac{50}{100} R$ = $\frac{50}{100} R$

Original area = $\frac{R}{2}$ and new area = ${πR}^{2}$

$\frac{3 {πR}^{2}}{4} * \frac{1}{{πR}^{2}} * 100$

Decrease in area = $π {(\frac{R}{2})}^{2} = \frac{{πR}^{2}}{4}$ = 75%

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