1. A rectangular lawn 55 m by 35 m has two roads each 4 m wide running in the middle of it, one parallel to length and the other parallel to breadth. The cost of gravelling the roads at 75 paise per sq. meter is?

A. Rs. 254.50 B. Rs.258 C. Rs.262.50 D. Rs. 270

Answer Answer: Option B Explanation: Area of crossroads = (55 * 4 + 35 * 4 - 4) m^2 = 344 m^2.
Therefore cost of gravelling = Rs. (344 * 75/100) = Rs. 258.

2. The sides of a rectangular field are in the ratio 3:4. If the area of the field is 7500 sq.m, the cost of fencing the field @ 25 paise per meter is?

A. Rs.55.50 B. Rs.67.50 C. Rs.86.50 D. Rs. 87.50

Answer Answer: Option D Explanation: Let length = (3x) meters and breadth = (4x) meters.
Then, 3x * 4x = 7500 <=> 12x^2 = 7500 <=> x^2 = 625 <=> x = 25
So, length = 75 m and breadth = 100 m
Perimeter = {2(75 + 100)} m = 350 m
Therefore cost of fencing = Rs. (0.25 * 350) = Rs. 87.50.

3. A rectangular grassy plot 110 m 65 m has a gravel path 2.5 m wide all round it on the inside. Find the cost of gravelling the path at 80 paise per sq. metre?

A. Rs. 680 B. Rs. 700 C. Rs. 600 D. Rs. 780

Answer Answer: Option A Explanation: Area of the plot = (110 * 65) m^2 = 7150 m^2
Area of the plot excluding the path = {(110 - 5) * (65 - 5)} m^2 = 6300 m^2
Therefore area of the path = (7150 - 6300) m^2 = 850 m^2
Cost of gravelling the path = Rs. (850 * 80/100) = Rs. 680

4. If a parallelogram with area P a rectangle with area R and a triangle with area T are all constructed on the same base and all have the same altitude, then which of the following statements is false?

A. P = R B. P+T = 2R C. P = 2T D. T = (1/2) R

Answer Answer: Option B Explanation: Let each have base = b and height = h. Then, P = b*h, R = b*h, T = 1/2*b*h
So, P = R, P = 2T and T = 1/2 are all correct statements.

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

A. 40 B. 50 C. 120 D. None of these

Answer Answer: Option D Explanation: Let breadth = x meters. Then, length = (x+20) meters.
Perimeter = (5300/26.50) m = 200 m
Therefore 2{(x + 20) + x} = 200 <=> 2x + 20 = 100 <=> 2x = 80 <=> x = 40.
Hence, length = x + 20 = 60 m.