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The pearls of the maharaja

The pearls of the maharaja

A distinguished Indian maharajah left her precious pearl collection in inheritance to her daughters. In the will clearly specified the distribution method that would be the following:

The eldest daughter would receive a pearl plus one seventh of the rest of the pearls, the second daughter had to receive two pearls plus one seventh of the rest, the third daughter three pearls plus one seventh of the rest and so on until they were distributed among all her daughters.

It was agreed that they all took the same number of pearls

How many daughters did the maharajah have?

Solution

If we call X the number of pearls we have that the eldest daughter stays with and therefore will remain:

The second daughter will therefore stay with

As we know that both quantities are the same, we equate the equations and it remains that the Maharaja distributed 36 pearls. Substituting in the first equation we can obtain the number of pearls that the firstborn daughter took and since all the daughters took the same amount we have.