Two cities Alipur and Balipur are 72 km apart. Arun and Varun who stay at…
2024
Two cities Alipur and Balipur are 72 km apart. Arun and Varun who stay at Alipur start riding on bicycles to Balipur. Arun travels at a speed of 17 kmph while Varun's speed is 2 kmph more than Arun. Varun was riding faster, so he reaches Balipur early and returns immediately. On his way back he meets Arun at Chandipur Calculate total distance traveled by Varun before meeting Arun?
- A.
75 Kms
- B.
82 Kms
- C.
78 Kms
- D.
76 Kms
Attempted by 16 students.
Show answer & explanation
Correct answer: D
Speeds: Arun = 17 km/h, Varun = 19 km/h (17 + 2).
Let x be the distance (in km) Arun has ridden when they meet at Chandipur. Arun's travel time = x/17 hours.
Varun goes to Balipur (72 km) and then returns to the meeting point, so Varun's total distance before meeting = 72 + (72 - x) = 144 - x, and his time = (144 - x)/19 hours.
Equate times: (144 - x)/19 = x/17.
Solve: 17*(144 - x) = 19*x ⇒ 2448 - 17x = 19x ⇒ 2448 = 36x ⇒ x = 68 km.
Varun's total distance before meeting = 144 - x = 144 - 68 = 76 km.
Answer: 76 km