Question

If a student walks from his house to school at 5 kmph, he is late by 30 minutes. However, if he walks at 6 kmph, he is late by 5 minutes only. The distance of his school from his house is:
A) 2.5 km
B) 3.6 km
C) 5.5 km
D) 12.5 km

Answer 1

Hint: Here first we will assume the distance covered to be x and then will use the formula of speed to find the time taken in each case and then subtract each of the equations and find the required value of x.

Complete step-by-step answer:
Let the distance covered by the student be x.
The speed is given by:-
\[{\text{speed}} = \dfrac{{{\text{distance covered}}}}{{{\text{time taken}}}}\]
It is given that:
When student walks from his house to school at 5 kmph, he is late by 30 minutes
Therefore, speed is 5 kmph and time taken is 30 min
Hence according to the formula of speed we get:-
\[5 = \dfrac{x}{{30}}\]
\[ \Rightarrow \dfrac{x}{5} = 30\]……………………….(1)
Now it is given that when he walks at 6 kmph, he is late by 5 minutes only.
Therefore, here the speed is 6 kmph and time taken is 5 min
Hence according to the formula of speed we get:-
\[6 = \dfrac{x}{5}\]
\[ \Rightarrow \dfrac{x}{6} = 5\]…………………………(2)
Now we have subtract equation 2 from equation 1 in order to get the resultant time by which he is late
Hence on subtracting we get:-
\[\dfrac{x}{5} - \dfrac{x}{6} = 30 - 5\]
\[ \Rightarrow \dfrac{x}{5} - \dfrac{x}{6} = 25\]………………………………(3)
Now since the speed is given in kmph and the time taken is given in minutes
Hence we need to convert the minutes into hours.
Now we know that 1 hour has 60 min.
Therefore, 1 min will have \[\dfrac{1}{{60}}\] hours.
Hence 25 minutes will have \[\dfrac{1}{{60}} \times 25\] hours i.e. \[\dfrac{5}{{12}}\] hours
Hence substituting this value in equation 3 we get:-
\[\dfrac{x}{5} - \dfrac{x}{6} = \dfrac{5}{{12}}\]
Now taking LCM we get:-
\[\dfrac{{6x - 5x}}{{30}} = \dfrac{5}{{12}}\]
Solving it further we get:-
\[\dfrac{x}{{30}} = \dfrac{5}{{12}}\]
Solving for x we get:-
\[x = \dfrac{{5 \times 30}}{{12}}\]
\[ \Rightarrow x = 12.5km\]
Hence distance covered is 12.5 km

Therefore, option D is the correct option.

Note: Here students might forget to convert the time into hours which will lead to the wrong solution.
So the units in which the value is calculated should be the same as that of the given data.