Time, Speed and Distance Question 1 - CAT 2020
The distance from B to C is thrice that from A to B. Two trains travel from A to C via B. The speed of train 2 is double that of train 1 while traveling from A to B, and their speeds are interchanged while traveling from B to C. The ratio of the time taken by train 1 to that taken by train 2 in travelling from A to C is:
Step-by-Step Explanation
Let the distance from A to B be x; then the distance from B to C is 3x.
Segment AB: Train 1 travels at speed v, and Train 2 travels at speed 2v.
TimeāTrain 1ā = x/v
TimeāTrain 2ā = x/(2v)
Segment BC: The speeds are interchanged, so Train 1 travels at speed 2v, and Train 2 travels at speed v.
TimeāTrain 1ā = 3x/(2v)
TimeāTrain 2ā = 3x/v
Sum the times for each train across both legs:
Total TimeāTrain 1ā = x/v + 3x/(2v) = 5x/(2v)
Total TimeāTrain 2ā = x/(2v) + 3x/v = 7x/(2v)
Ratio = [5x/(2v)]/[7x/(2v)] = 5 : 7
Correct Option: A
š” FundaMakers Tip:
When a problem contains only ratios of distances and speeds, avoid variables entirely by assuming smart values. Let distance AB = 1 and BC = 3. Let Train 1's initial speed be 1, making Train 2's speed 2.
Train 1 Total Time = 1/1 + 3/2 = 2.5 hours.
Train 2 Total Time = 1/2 + 3/1 = 3.5 hours.
Ratio = 2.5 : 3.5 = 5 : 7. Assuming numbers converts abstract algebra into mental arithmetic.