CA Foundation · Quantitative Aptitude · Equations
A train travels 120 km at a uniform speed. If its speed had been 10 km/h more, it would have taken 1 hour less for the journey. What is the original speed of the train?
The original speed is 30 km/h. The condition 120/x − 120/(x + 10) = 1 reduces to x² + 10x − 1200 = 0, whose positive root is 30. At 30 km/h the trip takes 4 hours and at 40 km/h it takes 3 hours.
- A30 km/h
- B50 km/h
- C40 km/hCorrect
- D60 km/h
Explanation
Let the speed be x km/h. Then 120/x − 120/(x + 10) = 1, so 1200 = x(x + 10), giving x² + 10x − 1200 = 0. This factors as (x + 40)(x − 30) = 0, so x = 30. Check: 120/30 = 4 h and 120/40 = 3 h, a difference of 1 h. So the original speed is 30 km/h; 40 km/h is the increased speed.
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