Question

If a person walks at $14 km/hr$ instead of $10 km/hr$, he would have walked $20 km$ more. The actual distance travelled by him is:
A. 50 km
B. 56 km
C. 70km
D. 80 km

Answer 1

Hint: In this question, the person walks at $14 km/hr$ instead of $10 km/hr$ and hence he would have covered $20 km$ more distance. So the approach for solving this type of question is that time taken for two speeds is the same. Therefore the speed is directly proportional to the distance covered.

Formula used:

1. Distance $=$ Speed $\times $ Time

2. Distance $\propto$ Speed, where Time is a constant.

Complete step-by-step answer:
In the question, it is given that the person has to walk with speed = $10 km/hr$.

Let $s_1 = 10km/hr$ and 

Let the actual distance travelled when speed is 10 km/hr be $d_1= x$
But he walked at a speed of $14 km/hr$ and he would have covered $20 km$ more distance.

Let $s_2=14km/hr$ and

The Distance travelled when speed is 14 km/hr will be $d_2= x+20 km$.
So the time taken by the person to travel both distances is the same.
Travelling Time = constant.
We know the relationship between speed, distance travelled and time taken is given by:
${\text{Speed(S) = }}\dfrac{{{\text{Distance travelled(D)}}}}{{{\text{Time taken(t)}}}}.$
And we know that Time is constant. So we can write:
$  {\text{speed = k}} \times {\text{distance}} $

$   \Rightarrow \dfrac{{{{\text{s}}_1}}}{{{{\text{s}}_2}}} = \dfrac{{{{\text{d}}_1}}}{{{{\text{d}}_2}}} $
Substituting the values of speed and distance for two cases in above equation, we get:
$ \Rightarrow \dfrac{{10}}{{14}} = \dfrac{{\text{x}}}{{{\text{x + 20}}}} $

Simplifying for $x$,

$  10\left( {{\text{x + 20}}} \right) = 14{\text{x}} $

On further simplification,
$    {\text{14x - 10x = 200}} $
$   \Rightarrow {\text{4x = 200}} $

Dividing on both sides by $4$, we get
$   {\text{x = }}\dfrac{{200}}{4} = 50. $
Therefore, the actual distance travelled=50 km. So, option (A) is correct.

Note: In this type of question where the speed is changing from one value to another and distance is also changing. You should note in this type of question one quantity remains fixed i.e. in this case time is fixed. So next find the relationship between the remaining quantities. In this case speed is directly proportional to distance travelled.