Step 1: Initial situation
Let mass of man in M kg and speed is V , mass of boy is M/2 and speed of boy is V1
K.Eman=12(K.Eboy)
12MV2=12(12M2V21) ....(1)
Step 2: Final situation
Man speeds up by 1m/s so new speed of man =V+1
K.Eman=K.Eboy
12M(V+1)2=12(M2)V21 ....(2)
Step 3: Divide equation (1) by equation (2)
V2(V+1)2=12
⇒V=1√2−1
Hence option (C) is correct.