Question

Leaving home at the same time, Amal reaches office at 10: 15 am if he travels at 8 km/hr, and at 9: 40 am if he travels at 15 km/hr. Leaving home at 9: 10 am, at what speed, in km/hr, must he travel so as to reach office exactly at 10 am?

• A. 13
• B. 14
• C. 12
• D. 11

Answer 1

The Correct Option is C

Let the speed in the first two cases be s and the distance be \(d\). 
Given,
\(\frac{d}{8}-\frac{d}{15} = \frac{35}{60} ⇒ d = 10\; km\)
Required speed = \(\frac{10}{\frac{50}{60}}\) = \(12\) kmph
So, the correct option is (C) : 12.

Answer 2

Given :
Timing to reach the office at the speed of 15 km/h and 8 km/h are 9:40 AM and 10:15 AM respectively.
Now , the difference between the time taken to reach the office = 35 minutes
Let's assume the distance to the office from the home be x km
Therefore, we get the relation to calculate the time as follows :
\((\frac{x}{8})-(\frac{x}{15})=\frac{35}{60}\)
⇒ x = 10 km
Let's assume y kmph be the speed to reach the office in 50 minutes , then
\(\frac{10}{y}=\frac{50}{60}\) , x = 12
Therefore , the correct option is (C) : 12.