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CAT 2003 Slot 2 — QA Question 6

Basics of TSD/ProportinalityEasy

Two straight roads R1 and R2 diverge from a point A at an angle of 120°. Ram starts walking from point A along R1 at a uniform speed of 3 km/hr. Shyam starts walking at the same time from A along R2 at a uniform speed of 2 km/hr. They continue walking for 4 hours along their respective roads and reach points B and C on R1 and R2, respectively. There is a straight line path connecting B and C. Then Ram returns to point A after walking along the line segments BC and CA. Shyam also returns to A after walking along line segments CB and BA. Their speeds remain unchanged. The time interval (in hours) between Ram’s and Shyam’s return to the point A is:

Answer & solution

  • A

    1019+263

  • 219+103

  • C

    19+263

  • D

    19+103

Solution

After 4 hours,

Distance travelled by Ram, AB = 4 × 3 = 12 km

Distance travelled by Shyam, AC = 4 × 2 = 8 km

Ram’s return path = BC + CA = (x + 8) km

Shyam’s return path = CB + BA = (x + 12) km

Now dropping perpendiculars from C and A to form the right triangle AOC,

In ΔAOC,

OA = AC sin30˚ = 8 × 1/2 = 4

OC = AC sin60° = 8 × 32=43

∴ BC = ((43)2+162)

BC = 304

BC = 419

Time taken by Ram to travel = BC+CA3=419+83 ...(i)

Time taken by Shyam to travel = BC+BA2=419+122 ...(ii)

∴ Time interval between the two reaching point A is (i) subtracted from (ii)

= 219+103

Hence, option (b).

CAT 2003 Slot 2 QA Q6: Two straight roads R 1 and R 2 diverge from a point A at an angle of 120°. Ram starts walking from point A — Solution | TheCATExam