CAT 2005 — QA Question 17
Answer the next 2 questions based on the information given below.
Ram and Shyam run a race between points A and B, 5 km apart. Ram starts at 9 a.m. from A at a speed of 5 km/hr, reaches B, and returns to A at the same speed. Shyam starts at 9:45 a.m. from A at a speed of 10 km/hr, reaches B and comes back to A at the same speed.
Four points A, B, C and D lie on a straight line in the X-Y plane, such that AB = BC = CD, and the length of AB is 1 metre. An ant at A wants to reach a sugar particle at D. But there are insect repellents kept at points B and C. The ant would not go within one metre of any insect repellent. The minimum distance in metres the ant must traverse to reach the sugar particle is
Answer & solution
- A
1 + π
- C
- D
5
The ant will not go into the circles with centers B and C and radius = 1 m
The minimum distance that the ant has to traverse = the distance of the path A-H-G-D
HG = 1 m
AH = GD = × Circumference of circle =
AH + GD = π m
∴ The ant must traverse (1 + π)m.
Hence, option (b).