*There are 3 persons Ram, Shyam and Ghanshyam. On some day, Ram lent books to Shyam and Ghanshyam as many as they had. After a month Shyam gave as many books to Ram and Ghanshyam as many as they had. After a month Ghanshyam did the same thing. At the end of this transaction each one of them had 24. Find the number of books each originally had?*

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Well, we can solve this puzzle by making 3 equations and then solving them simultaneously. That is a rather cumbersome process. Let us adopt an easier approach.
We know each has 24 books in the end. Since Ghanshyam gave Ram and Shyam as many books as they each had, it effectively means that the number of books they had doubled. This basically means that before Ghanshyam gave them the books, they had 12 books each. Now this also means that before
Ghanshyam gave them the books, he had 48 books (as he gave away 24 books and was left with 24 books). So the number of books Ram, Shyam and Ghanshyam had before Ghanshyam gave them away: 12, 12, 48.

Now Shyam had done that same thing, that is he gave 6 books to Ram and 24 books to Ghanshyam. So that means before the division effected by Shyam, the number of books held by Ram, Shyam and Ghanshyam were: 6, 42, 24.

Now Ram had also carried out the same process. That means he gave Shyam 21 books and Ghanshyam 12 books. So initially, Ram had 39 books, Shyam had 21 books and Ghanshyam had 12 books.