Rahul is going from Gurgaon to Agra from his car at the speed of 80 kmph. After 120 km, he reduces his speed by 12.5% and completes the whole journey in 5.5 hours. Find total time taken by him to cover the same distance, if he had reduced the speed after two hours.

The correct answer is 5$\frac{3}{7}$ hours.

Step 1: Calculate the time taken to cover the initial 120 km.
Initial speed of Rahul,

$S_1=80\text{ km/h}$

$D_1=120\text{ km}$

$t_1=\frac{120}{80}=1.5\text{ hours}$

Step 2: Calculate the reduced speed and the distance covered at reduced speed.
Rahul reduces his speed by 12.5%. Since

$12.5\%=\frac{1}{8}$

$S_2=80\times (1-\frac{1}{8})=80\times \frac{7}{8}=70\text{ km/h}$

$t_2=5.5-1.5=4\text{ hours}$

$D_2=70\times 4=280\text{ km}$

Step 3: Calculate the total distance of the journey.
Total distance:

$D=D_1+D_2=120+280=400\text{ km}$

Step 4: Calculate the total time if speed is reduced after 2 hours.
Distance covered in the first 2 hours at 80 km/h:

$D_a=80\times 2=160\text{ km}$

$D_b=400-160=240\text{ km}$

$t_b=\frac{240}{70}=\frac{24}{7}=3\frac{3}{7}\text{ hours}$

$T=2+3\frac{3}{7}=5\frac{3}{7}\text{ hours}$