A train has to travel the distance betwee… | Answer

Subject

Quantitative Aptitude

Topic

Speed & Distance

A train has to travel the distance between Mumbai and Chennai, equal to 1000 km, at a constant speed. It travelled half of the way with the specified speed and stopped for 2 hours, to arrive at Chennai on time, it had to increase its speed by 40 km/h for the rest of the way. What is the ratio between the train’s speed in first half and that in second half?
Reading

ক)

61 : 51

খ)

61 : 41

গ)

3 : 2

ঘ)

41 : 61

ঙ)

Can’t be determined

Explanation

Let the regular speed of the train = x km/hr. Now, time = distance/speed ∴ regular time taken by the train to travel the full distance = (1000/x) hrs Case-1: Distance travelled at regular speed = 1000/2 = 500km ∴ time taken to travel this distance = (500/x) hrs ---(1) Waiting time = 1 hour ⇒ for the remaining 500 kms, the train increases its speed by 40 km/h (i.e. x + 40) ∴ time taken to travel last 500 km = 500/(x + 40) ---(2) From the given data, we can clearly deduce that: Regular time = (time taken to travel first 500 km) + (waiting time) + (time taken to travel last 500 km)

\begin{array}{l} \Rightarrow \frac{{1000}}{x} = \frac{{500}}{x} + 2 + \frac{{500}}{{x + 40}}\\ \Rightarrow \frac{{500}}{x} - \frac{{500}}{{x + 40}} = 2\\ \Rightarrow \frac{{40}}{{{x^2} + 40x}} = \frac{2}{{500}} \end{array}

⇒x 2 + 40x – 10000 = 0 ⇒ D = b 2 – 4ac = 1600 - 4 × (-10000) = 41600 ⇒ x = (-b ± √D)/2a Omitting the negative value of speed, x = 81.98 ≈ 82 km/h ∴ x + 40 = 121.98 ≈ 122 km/h Required Ratio = 82 :122 = 41 : 61 Thus, required ratio is 41 : 61.

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Explanation

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