How many persons celebrate their birthday between Gupta

Solution

Garg celebrated his birthday on 15th of a month having less than 30 days. (so, Garg celebrates on 15th February). Person who celebrates his birthday on 15th March celebrates immediately after Singhal. (so, Singhal must celebrate on 5th March). Garg celebrates before Kansal and it is also given that only 2 persons celebrate between Garg and Kansal. Both Goyal and Bansal celebrate in the month having 31 days but there is a gap of 20 days between their birthdays. (Months having 31 days are either January and March, but there is no place in March, so both Goyal and Bansal celebrate their birthday in January, we get 2 possible cases here). Case-1 Only 3 persons celebrate between Garg and Mangal. Number of persons celebrating before Bansal is equivalent to number of persons celebrating after Bindal. Case-1 Case-2 Gupta celebrates his birthday after both Mittal and Jain. Therefore, Case 2 gets eliminated as it does not satisfy the given condition.