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Question Detail
The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:
 32%
 34%
 42%
 44%
Answer: Option D
Explanation:
Let original length = x metres and original breadth = y metres.
\begin{aligned}
\text{Original area } = \text{xy } m^2 \\
\text{New Length }= \frac{120}{100}x = \frac{6}{5}x \\
\text{New Breadth }= \frac{120}{100}y = \frac{6}{5}y \\
=>\text{New Area }= \frac{6}{5}x * \frac{6}{5}y \\
=>\text{New Area }= \frac{36}{25}xy \\
\text{Area Difference} = \frac{36}{25}xy  xy \\
= \frac{11}{25}xy \\
Increase \% = \frac{Differnce}{Actual}*100 \\
= \frac{11xy}{25}*\frac{1}{xy}*100 = 44\%
\end{aligned}
1. A courtyard is 25 meter long and 16 meter board is to be paved with bricks of dimensions 20 cm by 10 cm. The total number of bricks required is :
 16000
 18000
 20000
 22000
Answer: Option C
Explanation:
\begin{aligned}
\text{Number of bricks =}\frac{\text{Courtyard area}}{\text{1 brick area}} \\
= \left( \frac{2500 \times 1600}{20 \times 10} \right) \\
= 20000
\end{aligned}
2. One side of rectangular field is 15 meter and one of its diagonals is 17 meter. Then find the area of the field.
 \begin{aligned} 120m^2 \end{aligned}
 \begin{aligned} 130m^2 \end{aligned}
 \begin{aligned} 140m^2 \end{aligned}
 \begin{aligned} 150m^2 \end{aligned}
Answer: Option A
Explanation:
\begin{aligned}
\text{We know }h^2 = b^2+h^2 \\
=>\text{Other side }= \sqrt{(17)^2(15)^2} \\
= \sqrt{289225} = \sqrt{64} \\
= 8 meter \\
Area = Length \times Breadth \\
= 15\times8 m^2 = 120 m^2
\end{aligned}
3. The difference of the areas of two squares drawn on two line segments in 32 sq. cm. Find the length of the greater line segment if one is longer than the other by 2 cm.
 9 cm
 8 cm
 7 cm
 6 cm
Answer: Option C
Explanation:
Let the lengths of the line segments be x and x+2 cm
then,
\begin{aligned}
{(x+2)}^2  x^2 = 32 \\
x^2 + 4x + 4  x^2 = 32 \\
4x = 28 \\
x = 7 cm
\end{aligned}
4. A towel, when bleached, was found to have lost 20% of its length and 10% of its breadth. The percentage of decrease in area is ?
 25%
 26%
 27%
 28%
Answer: Option D
Explanation:
Let original length = x
and original width = y
Decrease in area will be
\begin{aligned}
= xy\left( \frac{80x}{100}\times\frac{90y}{100}\right) \\
= \left(xy \frac{18}{25}xy\right) \\
= \frac{7}{25}xy \\
\text{Decrease = }\left(\frac{7xy}{25xy} \times100\right) \% \\
= 28\%
\end{aligned}
5. What will be the cost of gardening 1 meter boundary around a rectangular plot having perimeter of 340 meters at the rate of Rs. 10 per square meter ?
 Rs. 3430
 Rs. 3440
 Rs. 3450
 Rs. 3460
Answer: Option B
Explanation:
In this question, we are having perimeter.
We know Perimeter = 2(l+b), right
So,
2(l+b) = 340
As we have to make 1 meter boundary around this, so
Area of boundary = ((l+2)+(b+2)lb)
= 2(l+b)+4 = 340+4 = 344
So required cost will be = 344 * 10 = 3440
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