This question involves the principle of conservation of momentum. According to this principle, the total momentum before a system has any external forces applied is equal to the total momentum after. Here, before the man jumps, the total momentum is zero as both man and boat are stationary. When the man jumps, his speed generates momentum in one direction, and the boat moves in the opposite direction to conserve total momentum.

Let`s denote M for mass of the man, B for mass of the boat.

According to the principle, M*5 = B*0.5; solving this equation we get B = M * 5 / 0.5 = M * 10

Option 4 - 10 times: This option is correct. The man`s mass must be 10 times less than the boat`s for the momentum to be conserved.

Option 1 - 5.5 times, option 2 - 4.5 times and option 3 - 2.5 times: All these options are incorrect as they don`t balance the momentum before and after the jump.