Question

A lady reaches her office $20$ minutes late by traveling at a speed of $20$ km/h and reaches $15$ minutes early by traveling at $30$ km/h. By how much time will she be early or late if she travels at $25$ km/h?

• A. $1$ minute early
• B. $5$ minutes early
• C. $1$ minute late
• D. $5$ minutes late

Answer 1

The correct option is A $1$ minute early

Let the distance of the office be $x$ km

Time taken at $20km/hr=\frac{x}{20}hrs$

Given that she reaches $\frac{20}{60}=\frac{1}{3}hrs$ late

Time taken at $30km/hr=\frac{x}{30}hrs$

Given that she reaches $\frac{15}{60}=\frac{1}{4}hrs$ early

$\therefore \frac{x}{20}-\frac{x}{30}=\frac{1}{3}+\frac{1}{4}$

$\Rightarrow x=35km$

Time taken at $30km/hr=\frac{35}{30}\times 60=70$ minutes

Time taken at $25km/hr=\frac{35}{25}\times 60=84$ minutes

So travelling at $25km/hr$ she reaches $70+15-84=1$ minute early