Let the radius of circular field = r m.
Speed of person in m/s = 30/60 = 1/2m/s
According to the question,
[(2πr) /(1/2)] - [(2r)/(1/2)] = 30

Correct Option: B

Let the radius of circular field = r m.
Speed of person in m/s = 30/60 = 1/2m/s
According to the question,
[(2πr) /(1/2)] - [(2r)/(1/2)] = 30
⇒ 4πr - 4r = 30
⇒ [4 x (22/7) - 4]r =30
⇒ (125 - 4)r = 30
⇒ (8.5)r = 30
⇒ r = 30/8.5 = 3.5 m

The man takes 3600 s for 14.4 km
The man will take 88 s for
14.4 x (88/3600) = 352/1000 km = 352 m

Now, circumference of circular field = 352 m
⇒ 2πr = 352 m
2 x (22/7) x r = 352
⇒ r = 56 m

Therefore, area of the field = πr²

Correct Option: B

The man takes 3600 s for 14.4 km
The man will take 88 s for
14.4 x (88/3600) = 352/1000 km = 352 m

Now, circumference of circular field = 352 m
⇒ 2πr = 352 m
2 x (22/7) x r = 352
⇒ r = 56 m

Therefore, area of the field = πr²
= (22/7) x 56 x 56
= 8 x 22 x 56 m²
= 9856 sq m.

Let the length of rectangle = L m
∴ Breadth of rectangle = B m
Using conditions from the question,
L - B = 23 ....(i)
2(L + B) = 206
L + B = 103 ....(ii)

Then , area of rectangle = L x B

Correct Option: A

Let the length of rectangle = L m
∴ Breadth of rectangle = B m
Using conditions from the question,
L - B = 23 ....(i)
2(L + B) = 206
L + B = 103 ....(ii)

On adding Eqs. (i) and (ii), we get
2L = 126
⇒ L = 63 m
⇒ B = 103 - 63 = 40 m

Then , area of rectangle = L x B
= 63 x 40
= 2520 m² .

Let original radius be r.
Then, according to the questions,
π (r + 1)² - πr² = 22

Correct Option: C

Let original radius be r.
Then, according to the questions,
π (r + 1)² - πr² = 22
⇒ π x [(r + 1)² - r²] = 22
⇒ (22/7) x (r + 1 + r ) x (r + 1 - r) = 22
⇒ 2r + 1 = 7
⇒ 2r = 6
∴ r = 6/2 = 3 cm

Increase in circumference of circle = 5%
∴ Increase in radius is also 5%.
Now, increase in area of circle = 2a + (a²/100) %

Correct Option: B

Increase in circumference of circle = 5%
∴ Increase in radius is also 5%.
Now, increase in area of circle = 2a + (a²/100) %
Where, a = increase in radius= 2 x 5 + (5 x 5)/100 % = 10.25%