Car ‘X’ travels for 4 hours to reach from point A to B. Car ‘Y’ travels at the speed of 70 kmph to reach from point B to C in 3 hours. Distance travelled by car ‘X’ to cover point A to B is $\frac{1}{7}$th more than distance travelled by car ‘Y’. How much time will car ‘X’ takes to reach from point A to C?

To find the total time taken by car ‘X’ to travel from point A to point C, we first need to determine the distances between the points and the speed of car ‘X’.

Step 1: Calculate the distance from B to C
Car ‘Y’ travels from point B to C at a speed of 70 kmph for 3 hours.
Using the formula:
$\text{Distance}=\text{Speed}\times \text{Time}$
We get the distance from B to C ($D_{\text{BC}}$):
$D_{\text{BC}}=70\text{ km/h}\times 3\text{ hours}=210\text{ km}$

Step 2: Calculate the distance from A to B
The distance covered by car ‘X’ from A to B ($D_{\text{AB}}$) is $\frac{1}{7}$ th more than the distance travelled by car ‘Y’ (which is $D_{\text{BC}}$).
Therefore:
$D_{\text{AB}}=D_{\text{BC}}+\frac{1}{7}\times D_{\text{BC}}$
Substituting the value of $D_{\text{BC}}=210\text{ km}$:
$D_{\text{AB}}=210+\frac{1}{7}\times 210$
$D_{\text{AB}}=210+30=240\text{ km}$

Step 3: Calculate the speed of car ‘X’
Car ‘X’ takes 4 hours to travel the distance $D_{\text{AB}}$ (240 km).
The speed of car ‘X’ ($S_{\text{X}}$) is:
$S_{\text{X}}=\frac{D_{\text{AB}}}{\text{Time}}=\frac{240}{4}=60\text{ kmph}$

Step 4: Calculate the total time taken by car ‘X’ to travel from A to C
The total distance from A to C is:
$D_{\text{AC}}=D_{\text{AB}}+D_{\text{BC}}=240+210=450\text{ km}$
The time required for car ‘X’ to cover this total distance at its speed of 60 kmph is:
$\text{Total Time}=\frac{D_{\text{AC}}}{S_{\text{X}}}=\frac{450}{60}=7.5\text{ hours}$

Thus, car ‘X’ will take 7.5 hours to reach from point A to C.