Question

A train covers 400 km at a uniform speed. If the speed had been 10 km/h more, it would have taken 2 hours less for the same journey. What is the usual time taken (in hours) by it to complete the journey?
1. 12
2. 15
3. 8
4. 10

Answer 1

Correct Answer - Option 4 : 10

Given:

A train covers total distance = 400km

Formula Used:

Speed = Distance covered/Time taken

Calculation:

Let the speed of the train be x

Time taken by train = 400/x

Now, the increased speed of train be(x + 10)

Now, Time taken by train = 400/(x + 10)

According to the question;

Difference between time taken = 2 hours

⇒ 400/x - 400/(x + 10) = 2

⇒ 1/x - 1/(x + 10) = 2/400

\(\Rightarrow \frac{{\left( {x + 10 - x} \right)}}{{\left( {x + 10} \right)x}} = \frac{{1}}{200}\)

⇒ 10 × 200 = x² + 10x

⇒ x² + 10x = 2000

⇒ x² + 10x - 2000 = 0

⇒ x = - 50, 40

The speed of the train = 40 km/hr

Time taken by train = 400/40 = 10 hours

∴ The usual time taken by the train to complete the journey is 10 hours.