# A lady reaches her office 20 mins late by travelling at a speed of 20 km/h and reaches 15 mins early by travelling at a speed of 30 km/h. By how much time(early or late) will she reach her office if she travels at 25 km/h?

Nov 27, 2016

Travelling at $25$ km/hr she will reach $1$ mt early.

#### Explanation:

Let the distance of the office be $x$ Km
Time taken at $20$ km/hr is $\frac{x}{20}$ hr; reaches $\frac{20}{60} = \frac{1}{3}$hr=20mt late
Time taken at $30$ km/hr is $\frac{x}{30}$ hr; reaches $\frac{15}{60} = \frac{1}{4}$hr=15mt early
Therefore $\frac{x}{20} - \frac{x}{30} = \frac{1}{3} + \frac{1}{4} \mathmr{and} \frac{x}{60} = \frac{7}{12} \mathmr{and} x = \frac{7}{12} \cdot 60 = 35$Km
Time taken at $30$ km/hr is $\frac{35}{30} = \frac{35}{30} \cdot 60 = 70$mt
Time taken at $25$ km/hr is $\frac{35}{25} = \frac{7}{5} h r = \frac{7}{5} \cdot 60 = 84 m t$;
So travelling at $25$ km/hr she will reach $70 + 15 - 84 = 1$mt early.[Ans]