Subject
Quantitative Aptitude
Topic
Speed & Distance
A train starts from a Jaipur towards Delhi at 10 am. Another train starts from Delhi towards Jaipur at 11 am. Both reach their destinations at same time. At 1 pm, the sum of distances that had been travelled by them together is 90% of distance between Delhi and Jaipur. At what time did they reach their destinations?
A train starts from a Jaipur towards Delhi at 10 am. Another train starts from Delhi towards Jaipur at 11 am. Both reach their destinations at same time. At 1 pm, the sum of distances that had been travelled by them together is 90% of distance between Delhi and Jaipur. At what time did they reach their destinations?
ক)
2 pmখ)
3 pmগ)
3:30 pmঘ)
4 pmঙ)
5 pmExplanation
Suppose the trains reach T hours after 10 am at their destination. ⇒ Train towards Delhi took T hours and train towards Jaipur took (T – 1) hours to reach their destination. Let speed of train towards Delhi be S km/hr. Since, both trains travelled equal distances, speed will be inversely proportional to time. ⇒ Speed of train moving towards Jaipur = (ST)/(T – 1) At 1 pm, the sum of distances that had been travelled by them together is 90% of distance between Delhi and Jaipur. By 1 pm, train towards Delhi has travelled for 3 hours and train towards Jaipur has travelled for 2 hours. Also, distance between Jaipur and Delhi = ST ⇒ Sum of distances = 3 × S + 2 × (ST)/(T – 1) = (90/100) × ST ⇒ 3 + 2 × (T/(T – 1)) = 0.9T ⇒ 3T – 3 + 2T = 0.9T 2 – 0.9T ⇒ 0.9T 2 – 5.9T + 3 = 0 ⇒ 9T 2 – 59T + 30 = 0 ⇒ (9T – 5)(T – 6) = 0 This gives T = 5/9 hours or T = 6 hours. Since, 5/9 < 1, this case is not possible as first train would reach destination before 11 am, and hence cannot meet second train in between. ⇒ T = 6 hours ∴ Trains will reach their destinations at 6 hours after 10 am; i.e., at 4 pm.Related questions
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