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Two cross roads, each of width 10 m, cut at right angles through the center of a rectangular park of length 700 m and breadth 300 m and parallel to its sides. The
area of the roads and the area of the park excluding cross roads respectively are. (Area should be in hectares).

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0.99 hectares, 14 hectares

0.99 hectares, 20.01 hectares

0.45 hectares, 21 hectares

0.98 hectares, 13 hectares

answer is B.

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Detailed Solution

Given two cross roads, each of width 10 m, cut at right angles through the center of a rectangular park of length 700 m and breadth 300 m and parallel to its sides.
Area of the park is

= 700 m × 300 m = 2, 10, 000 m 2

Now, area in hectare is
1 hectare = 10000

m 2

.
1

m 2

1 10, 000

hectares
Converting area of park in hectares,
210000

m 2

2, 10, 000 10, 000

hectares
= 21 hectares
Area of road 1,
Length = 700m
Breadth = 10m

= 700 m × 10 m = 7, 000 m 2

Area of road 2,
Length = 300m
Breadth = 10m

= 300 m × 10 m = 3, 000 m 2

Since, the cross section of roads is considered 2 times, we have to subtract it once.
Area of cross section is

= 10 m × 10 m = 100 m 2

Area of road = area of road 1 + area of road 2 – area of cross section
= 7000

m 2

+ 3000

m 2

- 100

m 2

=10000

m 2

- 100

m 2

= 9900

m 2

Now, we have to convert area into hectares,
1 hectare = 10000

m 2

m 2

1 10, 000

hectares
9900

m 2

9900 10, 000

hectares
= 0.99 hectares
Area of park without the roads is
= area of park – area of roads
= 21 hectares – 0.99 hectares
= 20.01 hectares
Area of roads is 0.99 hectares and the area of park without roads is 20.01 hectares.
Hence, option 2 is correct.

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