# Time and Speed Puzzle

Raja’s office is 9 km from his home. One day, he decided to jog to work in order to increase his fitness. He estimates the journey time to be a little over 1 hour 45 minutes.

At first he feels fine, but before long his energy beings to fade and he realizes he will not be able to run the whole distance. A passing taxi is the answer to his prayer. Raja hails the cab and completes his journey, arriving at work one hour 10 minutes earlier than he had anticipated.

Assuming Raja could at 1/6 the speed of the cab, how far did he run before he hailed the taxi?

10 Comments

Thanks Guys for the interesting discussion

We agree with Ashish Kumar’s explanation. Poor Raja could only manage to run 1.8 Km before he had to hail the taxi.

@Mohit: Suggestion well appreciated. Now onwards for dicey questions like this we will provide you the options.

yeah u r rite.i was also the victim of not having read dat “a little over” phrase

Frankly put, for such questions, you need 4 options

A) 2 KM

B) 1.8 KM

C) 8 KM

D) 2.5 KM

Usually in CAT they put such questions to create confusion, as many people do not read between lines. And you have to choose the best answer.

Awaiting Admin’s reply, as the examiner has the last word

then this question does not have an unique answer. his jogging speed could well be 4.9 kph b’coz “a little” can not be quantified.

how exactly did u then calculate???

“a little over” 1 hour 45 minutes to travel 9 km.

At 5 kph, to cover 9 km. Raja would have taken 1 Hr. 48 Min (a little over 1 hr. 45 min.)

let speed be x m/s.

by jogging he would have reached in 1 hr 45 mins=105 mis.

he reaches 1 hr 10 mins earlier i.e. 70 mins earlier. hence, he takes 105-70=35 mins.

let time of jogging = a mins. hence, time travelled by taxi = (35-a) mins.

equating distance covered(i.e. to the office) by jogging alone to distance covered by jogging as well as taxi,

105*x=a*x+(35-a)*6x

a=21 mins.

speed of jogging = 9000/(105*60)m/s

hence distance covered by jogging= speed * time= 9000 * 21/(105)= 1800 m= 1.8 km.

Time: 38 min.

Raja’s jogging speed = 5 kph

Car speed = 30 kph

2 km jog: Time = 24 min

7 km car: Time = 14 min

Hence, Raja jogged for 2 km.

Answer is 8 KM

1.8KM