Question

A man travels one third of the total distance by foot. He rides in a bus and covers two thirds of the distance by bus. If the distance covered by Bus was 100 km, then what was the total distance travelled by him?

Answer 1

Hint: We start solving the problem by assigning the variable for the total distance covered by the man. We then find the total distance covered by foot and total distance covered by bus in terms of the variable that we just assigned. We then equate the obtained equation of total distance covered by bus with the value given in the problem. We then make subsequent calculations in order to get the required value.

Complete step-by-step answer:
According to the problem, we had a man who travels one third of the total distance by foot and covers two thirds of the distance by bus. We need to find the total distance covered if he travelled 100 km by bus.
Let us assume the total distance covered by man be x km. From the information given in the problem we covered $\dfrac{x}{3}$km (one third of total distance) by foot and covered $\dfrac{2x}{3}$km (two third of total distance) by bus ---(1).
But we have already given that he travelled 100km by bus. So, we equate 100km with $\dfrac{2x}{3}$km that we have just obtained.
So, we have $\dfrac{2x}{3}=100$.
$\Rightarrow x=100\times \dfrac{3}{2}$.
$\Rightarrow x=50\times 3$.
$\Rightarrow x=150$km, which is the total distance travelled by man.
We have got a total distance covered by him of 150km.
∴ The total distance covered is 150km.

Note: We should not confuse and interchange the equations of the distance travelled in terms of the variable. We should not make mistakes while calculating the total distance covered. We can also find the distance covered by foot after obtaining the total distance covered. Similarly, we can expect problems to solve the total distance by giving the percentages covered by him with different sources of transportation.