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Only allegation method please

Expert replies
by seema19 » Wed Oct 12, 2011 9:38 am
A man covered a distance of 2000 km in 18 hrs partly by bus at 72 kmph and partly by train at 160 kmph. The distance covered by the bus is:
1) 1280 km
2) 720 km
3) 860 km
4) 640 km
5) 320 km

Answer: 2

Can someone please let me know how to solve this using allegation method.
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Source: — Problem Solving |

by GmatKiss » Wed Oct 12, 2011 9:50 am
A man covered a distance of 2000 km in 18 hrs partly by bus at 72 kmph and partly by train at 160 kmph. The distance covered by the bus is:

1) 1280 km
2) 720 km
3) 860 km
4) 640 km
5) 320 km

Its clear that, the answer should be 72*5 or 72*10 or 72*15

Try,

a)72*5 = 360 , remaining (2000-360) = 1640 (cannot be the distance by train)
b)72*10 = 720, remaining (2000-720) = 1280 (takes 8 hrs for train) - success!!

IMO: 2
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by leonswati » Wed Oct 12, 2011 10:12 am
You can solve it using allegation method but that would be time consuming... However..

Rate Rate Rate Time time Distance

Bus Bus 72 time 18-t time d

Trainbus 160 time t time 2000-d


Therefore total distance

160t + 72(18-t)= 2000

therefore t = 8

and total distance traveled by bus is (18-t)*72 = 10*72 = 720
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