Multiple choice

Directions for question: M and N start from X towards Y at 8 am with speeds 60 kmph and 50 kmph, respectively. After reaching Y, they spend 1 hour (individually) and then go back to X. M meets N at 30 km from Y, when M was returning to X, while N is still going to Y. What is the distance between X and Y?

  1. 550 km

  2. 600 km

  3. 630 km

  4. 1100 km

  5. cannot be determined
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let distance be D. M travels D + 30 km, N travels D - 30 km. M's speed = 60, N's speed = 50. Time taken by M = (D+30)/60 + 1 (break). Time taken by N = (D-30)/50. Since they meet when N is still going to Y, the times are equal. (D+30)/60 + 1 = (D-30)/50. (D+90)/60 = (D-30)/50. 5D + 450 = 6D - 180. D = 630 km.

AI explanation

Using the relative speed concept, since M travels at 60 kmph and N at 50 kmph, M finishes his onward journey of D kilometers in D divided by 60 hours, rests for 1 hour, and meets N 30 km away from Y, meaning M travels D minus 30 km in total. The equation for M's total travel time is D divided by 60 plus 1 plus 30 divided by 60, while N's travel time to the meeting point is D minus 30 divided by 50. Setting these equal gives D divided by 60 plus 1.5 equals the quantity D minus 30 divided by 50, and solving this yields D equals 630 km.

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