Friday, 24 July 2015

Concept of “Alligation”-04

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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