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

This problem involves two different strategies for using multiple transport modes:

Amal's strategy: Uses each transport for equal time periods

Bimal's strategy: Uses each transport for equal distance segments

We need to compare their total travel times.

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To make calculations easier, let's assume the total distance from A to B is 60 km.

Why 60 km? Because it's divisible by 3, which will make our "1/3 of distance" calculations clean.

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Bimal travels $\tfrac{1}{3}$ of total distance using each transport mode.

Since total distance = 60 km, Bimal travels 20 km at each speed.

Using Time = Distance ÷ Speed:

At 10 kmph: Time = 20 ÷ 10 = 2 hours

At 20 kmph: Time = 20 ÷ 20 = 1 hour

At 30 kmph: Time = 20 ÷ 30 = $\tfrac{2}{3}$ hour

Bimal's total time = 2 + 1 + $\tfrac{2}{3}$ = 3$\tfrac{2}{3}$ hours = 3 hours 40 minutes = 220 minutes

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Amal travels for $\tfrac{1}{3}$ of his total travel time using each transport mode.

Let Amal's total time = T hours

Then he uses each transport for $\tfrac{T}{3}$ hours.

Using Distance = Speed × Time:

At 10 kmph: Distance = 10 × $\tfrac{T}{3}$ = $\tfrac{10T}{3}$ km

At 20 kmph: Distance = 20 × $\tfrac{T}{3}$ = $\tfrac{20T}{3}$ km

At 30 kmph: Distance = 30 × $\tfrac{T}{3}$ = $\tfrac{30T}{3}$ km

Total distance = $\tfrac{10T}{3}$ + $\tfrac{20T}{3}$ + $\tfrac{30T}{3}$ = $\tfrac{60T}{3}$ = 20T km

Since the total distance is 60 km:

20T = 60

T = 3 hours

Amal's total time = 3 hours = 180 minutes

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Difference in time = 220 - 180 = 40 minutes

Percentage by which Bimal's time exceeds Amal's time:

= $\tfrac{40}{180}$ × 100 = 22.22%

Rounding to the nearest whole number: 22%

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Notice that Amal's approach is more efficient because he spends equal time at each speed, allowing him to cover more distance during the time spent on faster modes. Bimal's approach is less efficient because he covers equal distances at each speed, spending more time on slower modes.

Therefore, Bimal's travel time exceeds Amal's by approximately 22%.