If a train runs at 40 km/hour, it reaches its destination late by 11 minutes. But if it runs at 50 km/hours, it is late by 5 minutes only. The correct time (in minutes) for the train to complete the journey is

Options

A. 13
B. 15
C. 19
D. 21

Answer

To solve the problem step by step, we will first set up the equations based on the information provided.

### Step 1: Define Variables
Let:
- \( D \) = Distance to the destination (in km)
- \( T \) = Correct time to complete the journey (in hours)

### Step 2: Write Equations for Each Speed
1. When the train runs at 40 km/h, it is late by 11 minutes. This means:
\[ \frac{D}{40} = T + \frac{11}{60} \]
(Converting 11 minutes to hours: \( \frac{11}{60} \))

2. When the train runs at 50 km/h, it is late by 5 minutes. This means:
\[ \frac{D}{50} = T + \frac{5}{60} \]
(Converting 5 minutes to hours: \( \frac{5}{60} \))

### Step 3: Rearranging the Equations
From the first equation:
\[ D = 40 \left( T + \frac{11}{60} \right) = 40T + \frac{440}{60} \]

From the second equation:
\[ D = 50 \left( T + \frac{5}{60} \right) = 50T + \frac{250}{60} \]

### Step 4: Set the Two Equations for Distance Equal
Now we can set the two expressions for \( D \) equal to each other:
\[ 40T + \frac{440}{60} = 50T + \frac{250}{60} \]

### Step 5: Simplify the Equation
Rearranging gives:
\[ 40T - 50T = \frac{250}{60} - \frac{440}{60} \]
\[ -10T = \frac{-190}{60} \]
\[ 10T = \frac{190}{60} \]
\[ T = \frac{190}{600} = \frac{19}{60} \text{ hours} \]

### Step 6: Convert Time to Minutes
To convert \( T \) into minutes:
\[ T = \frac{19}{60} \times 60 = 19 \text{ minutes} \]

### Final Answer
The correct time for the train to complete the journey is **19 minutes**.

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