Angela travels from town A to town T, 10 km away. When she's halfway, Betty starts from town B for T, 15 km away. When Betty is half way, Charlie starts from town C for T, 30 km away. When he's half way, Dave starts from town D for T, 40 km away. If their speeds are uniform and in the ratio 1:3:12:16, respectively, the last one to reach T will be

Correct option is D

Solution:

Let speed of Angela = 1 unit
So,

• Betty = 3 units
• Charlie = 12 units
• Dave = 16 units

We'll use the concept of relative time remaining from the point each one starts to determine who takes the longest.

Step-by-Step Timeline Approach:

Let’s define time taken from halfway point to the destination.

Angela:

• Distance = 10 km
• Speed = 1 unit
• Time = 10 / 1 = 10 units

So, when Angela covers 5 km (halfway), time taken = 5 / 1 = 5 units

Betty starts when Angela has taken 5 units

• Distance = 15 km
• Speed = 3 units
• Total time = 15 / 3 = 5 units
• To reach halfway (7.5 km), time = 7.5 / 3 = 2.5 units

So, Charlie starts at time = 5 + 2.5 = 7.5 units

Charlie starts at 7.5 units

• Distance = 30 km
• Speed = 12 units
• Total time = 30 / 12 = 2.5 units
• Halfway = 15 km → Time = 15 / 12 = 1.25 units

So, Dave starts at time = 7.5 + 1.25 = 8.75 units

Now calculate when each person reaches town T:

• Angela: Started at 0, total time = 10 / 1 = 10 units → reaches at 10 units
• Betty: Started at 5, time = 15 / 3 = 5 units → reaches at 10 units
• Charlie: Started at 7.5, time = 30 / 12 = 2.5 units → reaches at 10 units
• Dave: Started at 8.75, time = 40 / 16 = 2.5 units → reaches at 11.25 units

Final Comparison:

Final Answer: (D) Dave