Subject: General Aptitude · Chapter: Time and Distance · Exam: 2010 · Marks: · Difficulty:
A man covers a certain distance on a toy train. Had the train moved 4 km/hr faster, it would have taken 30 minutes less. If it moved 2 km/hr slower, it would have taken 20 minutes more. Find the distance.
Answer
Answer (as printed):
Explanation
Let the distance be x km and initial speed be y km/hr. x x 30 1 4x y2 + 4y Then, – = = ⇔ = 2 ⇔ 8x = y2 + 4y ⇔ x = ...(i) y y + 4 60 2 y( y + 4) 8 x x 20 1 2x 1 y2 – 2y And, – = = ⇔ = ⇔ 6x = y2 – 2y ⇔ x = ...(ii) y – 2 y 60 3 y( y – 2) 3 6 From (i) and (ii), we have : y2 + 4y y2 – 2y = ⇔ 6y2 + 24y = 8y2 – 16y ⇔ 2y2 = 40y ⇔ 2y = 40 ⇔ y = 20. 8 6 Putting y = 20 in (i), we get : x = 60. Hence, required distance = 60 km.
Explanation as extracted from the printed page; notation may be imperfect.