Question

Rajesh commutes daily by travelling \[\dfrac{4}{5}\] of the distance between his home and office by metro train, \[\dfrac{3}{{20}}\] by auto and remaining 1 km on foot. What is the distance between his home and office?

Answer 1

Hint: We will consider the total distance between his home and office be x kilometers. Then he travels \[\dfrac{4}{5}\] by metro and \[\dfrac{3}{{20}}\] by auto. But after covering this distance there remains only 1km. so we will subtract the distances travelled before from the total distance such that the remaining distance is 1km. so let’s solve it!

Complete step by step solution:
Let the total distance be x kilometers.
Now he travels \[\dfrac{4}{5}\] by metro train. Then \[\dfrac{3}{{20}}\] by auto. So total he travels \[\dfrac{4}{5}x + \dfrac{3}{{20}}x\]
Now we will take the LCM,
\[ = \dfrac{{4 \times 4}}{{5 \times 4}}x + \dfrac{3}{{20}}x\]
On multiplying we get,
\[ = \dfrac{{16}}{{20}}x + \dfrac{3}{{20}}x\]
On adding the numerators we get,
\[ = \dfrac{{19}}{{20}}x\]
This is the distance travelled.
Now the remaining distance is 1km. so we can say that,
\[x - \dfrac{{19}}{{20}}x = 1\]
Taking the LCM on LHS,
\[\dfrac{{20x - 19x}}{{20}} = 1\]
\[\dfrac{x}{{20}} = 1\]
On transposing we get,
\[x = 20km\]
This is the total distance between Rajesh home and office.
So, the correct answer is “20 km”.

Note: Note that the last distance given is the remaining distance after he completes the first two distances travelled. So we added the distance travelled and removed this from the total and it is the remaining distance. This is the only way to solve it.
But don’t make the mistake that adding the distances will give the total distances. It is not that simple!