Distance between A and B is 1200 km. If they start moving towards each other at same time, they will meet in 24 hrs. If A starts 10 hrs after B, then they will meet after another 20 hrs. What are their respective speeds?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e 30 km/h, 20 km/h.
Let speed of A = x km/h, speed of B = y km/h
When both start together, they meet in 24 hours.
So, (x + y) × 24 = 1200 ⇒ x + y = 50 ...(1)
When A starts 10 hours late, B travels alone for 10 hours, covering 10y km.
Then both travel together for 20 hours, covering 20(x + y) km.
Total distance = 10y + 20(x + y) = 1200 ⇒ 10y + 20x + 20y = 1200 ⇒ 20x + 30y = 1200
⇒ 2x + 3y = 120 ...(2)
From (1), x = 50 - y
⇒ 2(50 - y) + 3y = 120 ⇒ 100 - 2y + 3y = 120 ⇒ 100 + y = 120 ⇒ y = 20
⇒ x = 50 - 20 = 30