If a train runs at 40 km/h, it reaches its destination late by 11 min, but if it runs at 50 km/h, it is late by 5 min only. The correct time for the train to complete its journey is
Question
If a train runs at 40 km/h, it reaches its destination late by 11 min, but if it runs at 50 km/h, it is late by 5 min only. The correct time for the train to complete its journey is
Solution
Let's solve this step by step:
Step 1: Let's denote the distance of the journey as D (in km) and the correct time to complete the journey as T (in hours).
Step 2: According to the problem, we have two equations based on the speed, distance, and time relationship (D = speed * time):
- When the train runs at 40 km/h, it is late by 11 minutes, so the equation is: D = 40 * (T + 11/60)
- When the train runs at 50 km/h, it is late by 5 minutes, so the equation is: D = 50 * (T + 5/60)
Step 3: Since both equations are equal to D, we can set them equal to each other and solve for T:
40 * (T + 11/60) = 50 * (T + 5/60)
Step 4: Simplify the equation and solve for T:
40T + 440/60 = 50T + 250/60
40T - 50T = 250/60 - 440/60
-10T = -190/60
T = 190/600 = 0.3167 hours
Step 5: Convert the time from hours to minutes (since the problem is asking for the time in minutes):
0.3167 hours * 60 minutes/hour = 19 minutes
So, the correct time for the train to complete its journey is 19 minutes.
Similar Questions
If a train runs at 40 km/h, it reaches its destination late by 11 min, but if it runs at 50 km/h, it is late by 5 min only. The correct time for the train to complete its journey isA12 minB16 minC19 minD25 minSolutionThe correct option is C 19 minLet the correct time to complete the journey be x minutes.Distance covered in (x+11) min at 40 km/h.= Distance covered in (x+5) min at 50 km/h∴(x+11)60×40=(x+5)60×50⇒x=19minSuggest Corrections68SIMILAR QUESTIONSQ. Q40. If a train runs at 40 km/h, it reaches its destination late by 11 min, but if it runs at 50 km/h, it is late by 5 min only. The correct time for the train to complete its journey isQ. If a train runs at 40 km/hr, it reaches its destination late by 11 minutes, but if it runs at 50 km/hr, it is late by 5 minutes only. The correct time for the train to complete the journey isQ. If a train runs at 40 kmph it reaches its destination late by 11 minutes. But if it runs at 50 kmph it is late by 5 minutes only. Find the distance covered by the train.Q. Choose the correct answer from the alternatives given.If a train runs at 70 km/hr, it reaches its destination late by 12 minutes. But if it runs at 80 km/hr. it is late by 3 minutes. The correct lime to cover the journey isQ. If a train runs at 40 kmph, it reaches the destination 15 minutes late. But if the train runs at 50 kmph, it is late by 5 minutes. Find the distance covered by the train.View MoreRELATED VIDEOSSpeed-Distance-TimeQUANTITATIVE APTITUDEWatch in AppEXPLORE MOREMeeting PointOther Quantitative Aptitude
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