Question

One can use three different transports which move at 10, 20, and 30 kmph, respectively. To reach from A to B, Amal took each mode of transport 1/3 of his total journey time, while Bimal took each mode of transport 1/3 of the total distance. The percentage by which Bimal’s travel time exceeds Amal’s travel time is nearest to

• A. 21
• B. 22
• C. 20
• D. 19

Answer 1

The Correct Option is B

Step 1: Amal's Total Distance 
Let the total travel time be \( 3T \) hours.
Each segment takes \( T \) hours.
 

Distances covered in each mode:

• At 10 kmph: \( 10T \)
• At 20 kmph: \( 20T \)
• At 30 kmph: \( 30T \)

Total distance \( = 10T + 20T + 30T = 60T \) km

Step 2: Bimal's Travel Time
Bimal covers the same total distance: \( 60T \) km.
He divides the journey into three equal distances of \( \frac{60T}{3} = 20T \) km per mode. 
Time taken for each mode:

• At 10 kmph: \( \frac{20T}{10} = 2T \)
• At 20 kmph: \( \frac{20T}{20} = T \)
• At 30 kmph: \( \frac{20T}{30} = \frac{2T}{3} \)

Total time taken by Bimal \( = 2T + T + \frac{2T}{3} = \frac{11T}{3} \)

Step 3: Percentage Difference in Time
Amal's time = \( 3T \), Bimal's time = \( \frac{11T}{3} \)
Extra time taken = \( \frac{11T}{3} - 3T = \frac{2T}{3} \)

Percentage more = \( \left( \frac{\frac{2T}{3}}{3T} \right) \times 100 = \left( \frac{2}{9} \right) \times 100 = 22.22\% \)

Answer: 22%