Question

A man traveled from the village to the post-office at the rate of 25 kmph and walked back at the rate of 4 kmph. If the whole journey took 5 hours 48 minutes, find the distance of the post-office from the village?
A. 20km
B. 22km
C. 24km
D. 26km

Answer 1

Hint: In the given question, we have been given the time taken to go from the village to the post-office and back from the post-office to the village. Then, we have been given the time taken for each trip. We have to calculate the distance from the village to the post-office. We are not provided with the exact time of each trip, but only with the total time of the round trip. For this question, we are going to need to assume the time of one trip and apply the distance-speed-time formula and evaluate the answers by forming two equations and calculate the values.

Formula Used:
We are going to use the distance-speed-time formula, which is:
\[ \Rightarrow \] \[distance = speed \times time\]

Complete step-by-step answer:
In the given question, we have been given the total time for a round trip from the village to the post-office and then back again, which is 5h 48min or \[5\dfrac{4}{5}h\].
Now, let the distance from the village to the post-office be \[x{\rm{ km}}\].
Then, let the time taken from the village to the post-office be \[y{\rm{ hr}}\].
Then, the time taken from the post-office to the village is going to be \[\left( {5\dfrac{4}{5} - y} \right){\rm{ hr}}\].
So, \[25 \times y = x\]
or \[x = 25y\] …(i)
And, \[4 \times \left( {\dfrac{{29}}{5} - y} \right) = x\]
or, \[\dfrac{{116}}{5} - 4y = x\] …(ii)
Comparing equations (i) and (ii), we have:
\[ \Rightarrow \]\[\dfrac{{116}}{5} - 4y = 25y\]
Taking the \[4y\] to the other side,
\[ \Rightarrow \]\[\dfrac{{116}}{5} = 25y + 4y\]
Solving the two sides we have:
\[ \Rightarrow \]\[y = \dfrac{4}{5}\]
Putting \[y = \dfrac{4}{5}\] in equation (i), we have:
\[ \Rightarrow \]\[x = 25 \times \dfrac{4}{5} = 20\]
Hence, the required distance is \[20km\].

Hence, the correct option is A).

Note: So, for solving questions of such type, we first write what has been given to us. Then we write down what we have to find. Then we think about the formulae which contains the known and the unknown and pick the one which is the most suitable for the answer. Then we put in the knowns into the formula, evaluate the answer and find the unknown.