VeritasKarishma wrote:

A distance of 600 km is to be covered using both Train & Bus. If first 120 km are covered by train and rest by Bus, it takes 8 hr in all. However if the train is used for 80 km more, it takes 20 min more for the entire journey. What is the speed of train?

(A) 40 mph

(B) 45 kmph

(C) 50 mph

(D) 60 mph

(E) 72 mph

(Try to arrive at the answer using an elegant solution)

(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

_________________

Scott Woodbury-Stewart

Founder and CEO

GMAT Quant Self-Study Course

500+ lessons 3000+ practice problems 800+ HD solutions