Question

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

Answer 1

Hint: In this use the given information to make the required equation and also remember that time for both the cases will remain the same, using this additional information will help you to approach towards the solution of the given problem.

Complete step-by-step answer:
According to the given information we know that person is walking with speed of 10 km/hr
But if the person walks with speed of 14 km/hr then it covers the distance 20 km more compare to when he walks 10 km/hr
So let x be the distance covered by the person when he is walking with speed of 10 km/hr
So the distance of person walking at speed 14 km/hr = x + 20
Since we know that the time taken by person to cover a distance will be same
Using the equation which shows the relation between the distance, speed and time i.e. distance = speed $ \times $ time
So for the first case, speed = 10 km/hr, time = t and distance = x
Substituting the values in the formula we get
x = 10 $ \times $ t
$ \Rightarrow $ t = $\dfrac{x}{{10}}$ equation 1
Now for second case speed = 14 km/hr, time = t and distance = x + 20
Substituting the values in the formula we get
x + 20 = 14 $ \times $t
$ \Rightarrow $ t = \[\dfrac{{x + 20}}{{14}}\] equation 2
Equating equation 1 and equation 2 we get
 $\dfrac{x}{{10}}$ = \[\dfrac{{x + 20}}{{14}}\]
$ \Rightarrow $ 14 x = 10 x + 200
$ \Rightarrow $14x – 10x = 200
$ \Rightarrow $ 4x = 200
$ \Rightarrow $x = $\dfrac{{200}}{4}$
$ \Rightarrow $ x = 50 km
Therefore the actual distance travelled by the person walking at speed of 10 km/hr is 50 km
Hence option A is the correct option.

Note: In the above solution we made the equations using the given information where the equations were linear equation with 1 variable which can be explained as the equation which contains only one variable the general representation of linear equation in one variable is given as ax + b = 0 here a and b are the integers and x is the variable in the equation which means that its value is unknown, these equations have only one solution there are more types of equations such as linear equation of 2 variables which have only 2 dissimilarities than linear equation in 1 variable that are linear equations with 2 variables consist of 2 variables and it consists of more than 1 solution.