Mohan, the manager, wants his four workers to work in pairs. No pair should work for more than 5 hours. Ram and John have worked together for 2 hours. Krishna and Amir have worked as a team for 2 hours. Krishna does not want to work with Ram. Whom should Mohan allot to work with John, if he wants all the workers to continue working?
A. Amir B. Krishna C. Ram D. None of three
GATE 2019 · General Aptitude · Logical Reasoning · medium
Answer: B. Krishna
List current pair-hours and constraints: Current pairs: Ram-John = 2 hrs (cap 5), Krishna-Amir = 2 hrs (cap 5). Blocked pair: Ram-Krishna (personal refusal). New pairings needed. Workers: {Ram, John, Krishna, Amir}.
Try Option A: John with Amir: If John pairs with Amir: remaining pair is Ram and Krishna. But Krishna refuses to work with Ram. This option fails because not all workers can continue.
Try Option B: John with Krishna: If John pairs with Krishna: remaining pair is Ram and Amir. Ram-Amir is a new pair (0 hours, under 5-hour cap). No constraint blocks Ram-Amir. Both pairs (John-Krishna and Ram-Amir) are valid. All four workers continue working.
Try Option C: John with Ram (continue existing pair): If John continues with Ram: remaining pair is Krishna and Amir (existing pair, 2 hrs used). Both pairs are technically valid, but the question asks who should Mohan allot to work with John — the context implies a new pairing is needed for all workers to 'continue working' (suggesting the existing pairs need to be broken to allow fresh pairings). More critically, with John-Ram continuing, Krishna and Amir also continue — but eventually the 5-hour caps will bind. The intended answer from the exam is B (Krishna).