books Exam Logical Reasoning

raju dealt some cards to ravi and himself from full pack of cards and laid the rest aside.raju then said to ravi "if you give me a certain number of cards, i will have 4 times as many cards as you have. If you. If i give same number of cards then.I will have thrice as many cards as you will have". Of the choices, which could represent the number of cards with raju ?

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ans:31
assume raju has 'x' cards, ravi has 'y' cards and the cards exchanged be 'z'
we will get x+z=4(y-z)
x-z=3(y+z)
on solving these two eqtns we wil get
x=31y/9, z=y/9
suppose z=1 then y=9 & x=31 which obeys the above equations.
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books Other Question

After losing the "Spot on the Forehead" contest, the two defeated Puzzle Masters complained that the winner had made a slight pause before raising his hand, thus derailing their deductive reasoning train of thought. And so the Grand Master vowed to set up a truly fair test to reveal the best logician amongst them.
He showed the three men 5 hats - two white and three black. Then he turned off the lights in the room and put a hat on each Puzzle Master's head. After that the old sage hid the remaining two hats, but before he could turn the lights on, one of the Masters, as chance would have it, the winner of the previous contest, announced the color of his hat. And he was right once again.
What color was his hat? What could have been his reasoning?