Question
On which date Gupta celebrates his
birthday? Study the following information carefully and answer the given questions: 12 person ā Garg, Goyal, Bansal, Kansal, Singhal, Jindal, Bindal, Agarwal, Gupta, Mittal, Jain and Mangal celebrate their birthdays on 5th,15th and 25thof 4 different months ā January, February, March and April. Atleast 5 persons celebrate their birthdays between Bindal and Agarwal. Kansal celebrated his birthday after Garg. Gupta celebrates his birthday after both Mittal and Jain. Both Goyal and Bansal celebrate their birthday in a month having 31 days but there is a gap of 20 days between the birthdays of Goyal and Bansal. Only 2 persons celebrate their birthday between Garg and Kansal. 4 persons celebrate their birthday between Mittal and Jain. Number of people celebrating their birthday before Mangal is equivalent to number of people celebrating their birthday after Jindal. Person who celebrates his birthday on 15th March celebrates immediately after Singhal. Agarwal celebrateĀ his birthday before Garg. Only 3 persons celebrated their birthday between Garg and Mangal. Number of persons celebrating their birthday before Bansal is equivalent to number of persons celebrating their birthday after Bindal. Garg celebrated his birthday on 15th of a month having less than 30 days.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. 
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