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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

Explanation:**Let length = 3x metres and breadth = 4x metre.**

Now, area = (1/4)x 10000 sq.m = 2500sq.m

So, 3x × 4x = 2500 =>12x2 = 2500 =>

Therefore Length = 3x = 3(25/√3) m = 75/√3 m and Breadth = 4(25/√3) m = 100/√3m.

Now, area = (1/4)x 10000 sq.m = 2500sq.m

So, 3x × 4x = 2500 =>12x2 = 2500 =>

*x*= 25/√3Therefore Length = 3x = 3(25/√3) m = 75/√3 m and Breadth = 4(25/√3) m = 100/√3m.

- 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

Explanation:**Area of the carpet = Area of the room = (13 × 9) m**

Length of the carpet = (area/width) = 117 ×(4/3) m = 156 m.

Therefore Cost of carpeting = (156 × 12) = Rs.1872

^{2}= 117 m^{2}.Length of the carpet = (area/width) = 117 ×(4/3) m = 156 m.

Therefore Cost of carpeting = (156 × 12) = Rs.1872

- 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

Explanation:**Area of the plot = (100 x 70) m**

Area of the plot excluding the path = [(100 - 5) * (70 - 5)] m

Area of the path = (7000 - 6175) m

Cost of gravelling the path = Rs.825 * (90/100)= Rs.742.50

^{2}= 7000 m^{2}Area of the plot excluding the path = [(100 - 5) * (70 - 5)] m

^{2}= 6175 m^{2}.Area of the path = (7000 - 6175) m

^{2}= 825 m^{2}.Cost of gravelling the path = Rs.825 * (90/100)= Rs.742.50

- 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

Explanation:**Side of first square = (80/4) = 20 cm;**

Side of second square = (64/4)cm = 16 cm.

Area of third square = [(20)

Side of third square = (144)

Required perimeter = (12 x 4) cm = 48 cm.

Side of second square = (64/4)cm = 16 cm.

Area of third square = [(20)

^{2}- (16)^{2}] cm^{2}= (400 - 256) cm^{2}= 144 cm^{2}.Side of third square = (144)

^{(1/2)}cm = 12 cm.Required perimeter = (12 x 4) cm = 48 cm.

- 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

Explanation:**Area of the room = (1147 x 777) cm**

Size of largest square tile = H.C.F. of 1147 cm and 777 cm = 37 cm.

Area of 1 tile = (37 x 37) cm

Number of tiles required =(1147×777)/(37×37)=651

^{2}.Size of largest square tile = H.C.F. of 1147 cm and 777 cm = 37 cm.

Area of 1 tile = (37 x 37) cm

^{2}.Number of tiles required =(1147×777)/(37×37)=651

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