A distance of 600 km is to be covered using both Train & Bus.

for a difference of 80 km the train is used in second scenario instead of bus thereby increasing time of travel by 20 minutes

i.e. train takes 20 mins more than bus for 80 km journey

i.e. train takes 20*6 mins more than bus for 80*6 km journey

i.e. train takes 120 mins more than bus for 480 km journey

i.e. if Train had covered entire 600 km then the time taken would have been = 8 Hours + 120 minutes = 10 hours

i.e. Speed of train = 600/10 = 60 kmph

Answer: Option D

I hope the method lives upto the expectation of word ELEGANT :D

my method is conventional one:
given total distance is 600km

case 1 120 km by train and 480 km by bus = 8hr journey ; 480 mins
speed of train be x and speed of bus y
so
120/x+ 480/y = 480
120y+480x=480xy--(1)

case 2:
200 km by train and 400 km by bus = 500 mins
or say
200y+400x=500xy --(2)

solve for x & y
x= 1 km per min or 60 kmph
and y = 1.33 km per min or 80 kmph
IMO D is correct..

Used a stupid method but here it is...

let time of train used be T
Speed of train: 120/T
Speed of Bus: 480/(8-T)
20minutes = 1/3 hour

[200/(120/T)] +[400/(480/T)]=8 1/3
200T/120 + 400(8-T)/480=8 1/3
10T/6 +5(8-T)/6=8.3
T=approx 2.

Speed of train 120/2=60mph

Absolutely GMATinsight! This is what I had in mind!
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Archit3110 and 2asc - Your methods are correct. They are just a bit time consuming.

The bus takes 20 mins extra for 80 kms extra. That means it will take 20*6 = 120 mins extra for 80*6 = 480 km extra.
What we mean is that if the bus were to cover the rest of the 480 kms too (after the initial 120 kms), the time taken would be 120 mins = 2 hrs extra.
So total time taken would be 8 + 2 = 10 hrs for the bus to cover the entire 600 kms.
This means the bus speed is 600/10 = 60 kmph
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It helps me to transform the equations into 'smaller numbers'.
Since:
x = speed of train
y = speed of bus
Eq I :
120/x + 480/y = 480 (divide all by 60)
2/x + 8/y = 8
2y +8x =8xy

Eq II:
200/x + 400/y = 500 (divide all by 100)
2/x + 4/y = 5
2y + 4x = 5xy

Subtract II from I:
4x = 3xy
y = 4/3
and
x = 1 km/min = 60km/h

VeritasKarishma But option D is 60 MPH not 60 KMPH

(Note:The answer choices should be in kph rather than mph.)

We see that the first distance by train is 120, and the second distance by bus is 480. Let r = the speed of the train, in mph, and let s = the speed of the bus, in mph. Thus, we have the equation for the time:

120/r + 480/s = 8

If the train is used for 80 km more, then it will travel for 120 + 80 = 200 km, and the bus will travel for 480 - 80 = 400 km. The additional 20 minutes for the trip brings the total time to 8 hours, 20 minutes, which is 8 + ⅓ hours, or 25/3 hours. Thus, we have:
200/r + 400/s = 8 + ⅓ = 25/3

Multiplying each of the equations by 3rs, we have:

360s + 1440r = 24rs (Eq. 1)

and

600s + 1200r = 25rs (Eq. 2)

Multiplying Eq. 1 by 5 and Eq. 2 by 3, we have;

1800s + 7200r = 120rs

and

1800s + 3600r = 75rs

Subtracting these two equations, we have:

3600r = 45rs

Dividing both sides by 45r, we have:

80 = s

Substituting this back to the very first equation, we have:

120/r + 480/80 = 8

120/r + 6 = 8

120/r = 2

r = 60

Answer: D
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