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

Correct Option: 1 (which corresponds to 21)

Let the total distance between A and B be $D$ km.

1. Amal's Journey:
Let Amal's total travel time be $T_A$ hours. He spends $\frac{T_A}{3}$ hours at each speed: 10 kmph, 20 kmph, and 30 kmph.
The total distance covered by Amal is:
$D=10\left(\frac{T_A}{3}\right)+20\left(\frac{T_A}{3}\right)+30\left(\frac{T_A}{3}\right)$
$D=\frac{T_A}{3}(10+20+30)=20T_A$
Thus, Amal's travel time is:
$T_A=\frac{D}{20}$

2. Bimal's Journey:
Bimal travels $\frac{D}{3}$ distance at each of the speeds: 10 kmph, 20 kmph, and 30 kmph.
Let Bimal's total travel time be $T_B$ hours.
$T_B=\frac{D/3}{10}+\frac{D/3}{20}+\frac{D/3}{30}$
$T_B=\frac{D}{3}\left(\frac{1}{10}+\frac{1}{20}+\frac{1}{30}\right)$
Find a common denominator (60):
$T_B=\frac{D}{3}\left(\frac{6+3+2}{60}\right)=\frac{D}{3}\left(\frac{11}{60}\right)=\frac{11D}{180}$

3. Comparing Travel Times:
We want to find by what percentage Bimal's time exceeds Amal's time:
$\text{Percentage Increase}=\left(\frac{T_B-T_A}{T_A}\right)\times 100\%$
$\text{Percentage Increase}=\left(\frac{T_B}{T_A}-1\right)\times 100\%$
Let's calculate the ratio of their times:

Substitute this back into the percentage increase formula:
$\text{Percentage Increase}=\left(\frac{11}{9}-1\right)\times 100\%=\frac{2}{9}\times 100\%\approx 22.22\%$

The value is nearest to 22%.