Question : The ratio of the outer and the inner circumference of a circular path is 5 : 4. If the path is 50 metres wide, then what is the radius of the inner circle?
Option 1: 250 metres
Option 2: 300 metres
Option 3: 200 metres
Option 4: 210 metres
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Correct Answer: 200 metres
Solution :
Let the radius of the inner and outer circumference be $r$ and $R$. According to the question, $\frac{2\pi R}{2\pi r}=\frac{5}{4}$ ⇒ $\frac{2\pi(r+50)}{2\pi r}=\frac54$ ⇒ $4(r+50)=5(r)$ ⇒ $4r+200=5r$ ⇒ $r = 200$ metres Hence, the correct answer is 200 metres.
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Question : The outer and inner diameters of a circular path are 728 m and 700 m respectively. The breadth of the path is:
Option 1: 7 m
Option 2: 28 m
Option 3: 14 m
Option 4: 20 m
Question : Directions: Prem starts to walk to school from his house and walks 400 metres to the north turns left and walks 100 metres; turns left and walks 200 metres and then turns left and walks 100 metres. How far is he away from his house?
Option 1: 100 metres
Option 4: 250 metres
Question : Which of the following statements is INCORRECT?
Option 1: The radius is the longest chord of a circle.
Option 2: The ratio of the circumference of two circles is equal to the ratio of their radii.
Option 3: The perpendicular drawn from the centre of the circle on the chord of the circle bisects the chord.
Option 4: Circles are congruent to each other if they have equal radii.
Question : If the circumference of a circle is 220 cm, then what is its radius?
Option 1: 26 cm
Option 2: 25 cm
Option 3: 35 cm
Option 4: 40 cm
Question : A rectangular park, 60 metres long and 40 metres wide, has two concrete crossroads running in the middle of the park, and the rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. metres, then the width of the road is:
Option 1: 3 metres
Option 2: 5 metres
Option 3: 6 metres
Option 4: 2 metres
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