Multiple choice

Persons R and S started travelling towards each other at the speed of r km/h from point X and s km/h from point Y, respectively. The distance between X and Y is 10 km. R started the journey at 9 a.m. while S started the journey at 9:30 a.m. They both met at 11 a.m. at point Z. What is the ratio of r and s, if both are positive integers?

  1. 2 : 3

  2. 2 : 1

  3. 3 : 2

  4. 1 : 2

  5. Cannot be determined
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

R travels from 9:00 to 11:00 (2 hours) at r km/h. S travels from 9:30 to 11:00 (1.5 hours) at s km/h. Total distance = 2r + 1.5s = 10. 4r + 3s = 20. For positive integers, if r=1, 3s=16 (no). If r=2, 3s=12, s=4 (ratio 2:4 = 1:2). If r=3, 3s=8 (no). If r=4, 3s=4 (no). The ratio is 1:2.

AI explanation

R travelled for 2 hours from 9 a.m. to 11 a.m., covering a distance of 2r kilometres. S travelled for 1.5 hours from 9:30 a.m. to 11 a.m., covering a distance of 1.5s kilometres. The total distance between X and Y is 10 km, giving the equation 2r plus 1.5s equals 10. Testing the given integer ratios, if r is 1 and s is 2, then 2 plus 3 equals 5, which is not 10; however, multiplying both sides of the ratio 1 to 2 by two gives r equals 2 and s equals 4, meaning the fundamental ratio of r to s is 1 to 2.

Keep practicing — related questions