Pintoo dealt some cards to Minto and himself from a full pack of playing cards andlaid the rest aside. Pintoo then said to Mintoo, "If you give me a certain number of your cards I will have 4 times as many cards as you have. If I give you the same numberof cards, I will have thrice as many cards as you have." How manycards did Pintoo have?

Let number of cards with Pintoo = $$x$$ and number of cards laid aside = $$z$$

=> Number of cards with Mintoo = $$(52-x-z)$$

Let number of cards exchanged = $$k$$

Acc. to ques, => $$(x+k)=4(52-x-z-k)$$

=> $$x+k=208-4x-4k-4z$$

=> $$5x+5k+4z=208$$ ---------------(i)

Similarly, $$(x-k)=3(52-x-z+k)$$

=> $$x-k=156-3x+3k-3z$$

=> $$4x-4k+3z=156$$ ----------------(ii)

By applying 3(i)-4(ii), we get : $$-x+31k=0$$

=> $$x=31k$$

Now, we know that $$y$$ is a constant greater than 0, also since there are only 52 cards, we have $$k=1$$

$$\therefore$$ Number of cards with Pintoo = $$x=31$$

=> Ans - (A)