# CAT Practice : Speed Time, Races

## Increasing Speed

Q.23: Raj was travelling to his hometown from Mumbai. He met with a small accident 80 Km away from Mumbai and continued the remaining journey at 4/5 of his original speed and reached his hometown 1 hour and 24 minutes late. If he had met with the accident 40 Km further, he would have been an hour late.
i) What is Raj's normal speed?
a) 20 Km/hr b) 15 Km/hr c) 30 Km/hr d) 25 Km/hr
ii) What is the distance between Mumbai and Raj's hometown?
a) 140 Km b) 200 Km c) 220 Km d) 250 Km

D. 25 Km/hr , C. 220 Km

## Detailed Solution

Scenario 1:

$\frac{5D1}{4s} - \frac{D1}{s} = 1 + \frac{24}{60}$ (always write minutes in this form if the unit is Km/hr)

=) $\frac{D1}{s} = \frac{7}{5} * 4 = \frac{28}{5}$hours

Scenario 2:

$\frac{5D2}{4s} - \frac{D2}{s} = 1$

=) $\frac{D2}{s} = 4$ hours

i) Therefore, in his normal speed, he can travel 40 Km in $\frac{28}{5} - 4 = \frac{8}{5}$hours so, s = $\frac{40}{\frac{8}{5}}$= 25 Km/hr. Answer d)

ii) $\frac{D1}{s} = \frac{28}{5}$ =) D1 = 140 Km. Therefore, total distance D = 140 + 80 = 220 Km.

Correct Answer: D. 25 Km/hr , C. 220 Km

## Our Online Course, Now on Google Playstore!

### Fully Functional Course on Mobile

All features of the online course, including the classes, discussion board, quizes and more, on a mobile platform.

### Cache Content for Offline Viewing

Download videos onto your mobile so you can learn on the fly, even when the network gets choppy!

## More questions from Speed Time, Races

"Life is a race ... if you don't run fast ... you will be like a broken undaa" - Veerusahasra Buddhi