Question

Arun, Biju and Cijo run along a circular park with the speeds of 8 km/hr, 5 km/hr and 3 km/hr respectively for 2 hours. If the circumference of the park is 500 metre, then how many times they will meet at starting points?
a) 2
b) 3
c) 4
d) 5

Answer 1

In the circle with centre O

∠AOB = 80° and ∠AOC =110°

∴ ∠BOC = ∠AOB + ∠AOC

= 80°+ 110°= 190°

∴ Reflex ∠BOC = 360° – 190° = 170°

Now arc BEC subtends ∠BOC at the centre and ∠BAC at the remaining part of the circle.

∴ ∠BOC = 2∠BAC

⇒ 170° = 2∠BAC

⇒ ∠BAC = 170∘2 = 85°

∴ ∠BAC = 85°