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- 6. A lawn is in the form of a rectangle having its sides in the ratio 3: 4. The area of the lawn is (1/4) hectares. Find the length and breadth of the lawn.
A.75,100
B.75/√3,100/√3
C.75, 100/√3
D.75/√3,100
Answer & Explanation
Answer: Option B 
Let length = 3x metres and breadth = 4x metre.
Now, area = (1/4)x 10000 sq.m = 2500sq.m
So, 3x × 4x = 2500 =>12x2 = 2500 => x = 25/√3
Therefore Length = 3x = 3(25/√3) m = 75/√3 m and Breadth = 4(25/√3) m = 100/√3m.
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- 7. Find the cost of carpeting a room 13 m long and 9 m broad with a carpet 75 cm wide at the rate of Rs.12 per square metre.
A.1824
B.1854
C.1872
D.1888
Answer & Explanation
Answer: Option C
Area of the carpet = Area of the room = (13 × 9) m2 = 117 m2.
Length of the carpet = (area/width) = 117 ×(4/3) m = 156 m.
Therefore Cost of carpeting = (156 × 12) = Rs.1872
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- 8. A rectangular grassy plot 100 m. by 70 m has a gravel path 2.5 m wide all round it on the inside. Find the cost of gravelling the path at 90 paise per sq. metre.
A.Rs.700
B.Rs.708.50
C.Rs.732.50
D.Rs.742.50
Answer & Explanation
Answer: Option D
Area of the plot = (100 x 70) m2 = 7000 m2
Area of the plot excluding the path = [(100 - 5) * (70 - 5)] m2 = 6175 m2.
Area of the path = (7000 - 6175) m2 = 825 m2.
Cost of gravelling the path = Rs.825 * (90/100)= Rs.742.50
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- 9. The perimeters of two squares are 80 cm and 64 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares.
A.42cm
B.44cm
C.46cm
D.48cm
Answer & Explanation
Answer: Option D
Side of first square = (80/4) = 20 cm;
Side of second square = (64/4)cm = 16 cm.
Area of third square = [(20)2 - (16)2] cm2 = (400 - 256) cm2 = 144 cm2.
Side of third square = (144)(1/2) cm = 12 cm.
Required perimeter = (12 x 4) cm = 48 cm.
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- 10. A room 11 m 47 cm long and 7m 77 cm broad is to be paved with square tiles. Find the least number of square tiles required to cover the floor.
A.636
B.640
C.647
D.651
Answer & Explanation
Answer: Option D
Area of the room = (1147 x 777) cm2.
Size of largest square tile = H.C.F. of 1147 cm and 777 cm = 37 cm.
Area of 1 tile = (37 x 37) cm2.
Number of tiles required =(1147×777)/(37×37)=651
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