Question: A person travels 285
km in 6 hours in two stages. In the first part of the journey, he travels by
bus at the speed of 40 km per hour. In the second part of the journey, he
travels by train at the speed of 55 km per hr. How much distance did he travel
by train? [Ans. (c) 165 km]
(a) 142.5 km (b) 180 km
(c) 165 km (d) 120 km (e) none of these
Solution:
Detailed
Solution:
Concept:
In the method of “Alligation”, rate of the two mixtures are taken and the rate
the final mixture (mixture of two mixtures) should also be given. Then, the
ratio of the quantity of two mixtures can be determined. Out of these four
variables, any variable can be determined, if all other three variables are
given.
In the given question, a distance
of 285 km is described in 6 hours in two stages. In the first part of the
journey, the man travels by bus at the speed of 40 km/hour. In the second part
of the journey, he travels by train at the speed of 55 km/hour.
The rate for the whole
journey is 285 km in 6 hours, that is, 47.5 km/hr.
Here, since the rate is
with respect to time, so in the method of “Alligation”, ratio of time will be
determined first and then distance described.
Solution:
By method of Alligation
Total distance described =
285 km
Total time taken = 6 hours
Bus (Km/h) Train (Km/h)
40 55
Mean (Km/h)
285/6 = 47.5
7.5 (55-47.5) : 7.5 (47.5-40)
Or, 1 :
1
[Total
time] = 2 ≡ 6 hours
[Time
for each] =1 ≡? = 3 hours
Distance (train) = 55×3 =
165 km. Ans.
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