# Solution with Explanations

Vijay, Bala and Vivek are three persons who can complete a work in 10,20 and 25 days respectively; What is the minimum number of days required to complete the work if only any  two persons among them work on the same day and no two consecutive days have the same pair of persons working?

The answer to be found out is the minimum number of days required for completion of the work subject to the two conditions that (i) only two persons among the three work on the same day and (ii) no two consecutive days have the same pair of persons working. Since number of days of work and efficiency of the persons on work are inversely proportional, it is obvious that the most efficient pair of persons should be engaged on each day, satisfying the two conditions, to  finish the work in minimum number of days.

Vijay and Bala together complete 1/10  + 1/20 parts of the whole work on a single day. i.e. 10/100 + 5/100  = 15/100 parts of the work.

Bala and Vivek together complete 1/20 + 1/25 parts of the whole work on a single day. i.e. 5/100 + 4/100  = 9/100 parts of the work.

Vivek and Vijay together complete 1/25 + 1/10 parts of the whole work on a single day. i.e. 4/100 and 10/100 =  14/100 parts of the work.

The common denominator 100 is taken to ensure easy comparison of the work efficiency. The LCM of 10,20 and 25 is 100.

It is observed that the order of efficiency of work  for a particular pair of persons is : Vijay and Bala -the most efficient; Vivek and Vijay-the second best; and Bala and Vivek- the least efficient. In order to complete the work in minimum number of days the first and second mentioned pair of persons should be engaged. The first pair of persons should not be engaged for two consecutive days to comply with one of the conditions mentioned in the problem. So, on two consecutive days the pair of persons Vijay and Bala and Vivek and Vijay should be put on work.

In two consecutive days the combined pair of persons will complete 15/100 + 14/100 = 29/100 parts of the work. This combination can be continued in satisfaction of  condition No.(ii) till the completion of the work. This combination will be able to complete 29 X 3 =87 parts out of 100 parts of the  work in 6 days. The remaining 13  parts  of the work will be done by the combination of Vijay and Bala in 13/15 days i.e. The work can be completed in   6 days and 13/15 of a day. This will be the minimum number of days required to complete the work with reference to the given conditions.

Article Courtesy :

Mr. Gopalakrishnan

33 years experienced CPSU Officer (Retd.)

He is an expert in handling General English, Quantitative Aptitude and Interview programs.

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