Question
A train 'D' departed from Lucknow
at 7:00 PM, traveling at a speed of 66 km/h, and reached Kolkata. Meanwhile, Train 'C' left Kolkata at 9:00 PM on the same day, moving at a speed of 58 km/h, and headed towards Lucknow. The two trains met at 2:00 AM. Which of the following statements is accurate? I. The time required for Train 'B', which travels at a speed of 47 km/h, to reach Kolkata from Lucknow is 'p hours. II. After meeting, the difference in the distance covered by Train 'D' and Train 'C' in exactly 2 hours is 'q' km. III. If Train 'C' maintained a constant speed for 12 hours, the distance it covered in that period is 'r' km less than the total distance between Lucknow and Kolkata.Solution
ATQ, Distance between Lucknow & Kolkata = 66 × 7 + 58 × 5 = 462 + 290 = 752 km I) p = 752/47 = 16 II) q = (66 - 58) × 2 = 8 × 2 = 16 III) r = 752 - 12 × 58 = 752 - 696 = 56 1.5p + 2q = r 1.5 × 16 + 2 × 16 = 56 24 + 32 = 56 56 = 56 LHS = RHS 1.5p + 2q = r
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