Mystery of Missing Money – 1 Rupee by Shakuntala Devi

In a busy marketplace, two women sell marbles differently: one sells three marbles for a Rupee, and the other sells two marbles for a Rupee. When they combine their unsold marbles and try to sell them together, they expect to make the same amount of money. But to their surprise, they end up one Rupee short.

This story, told by the famous math genius Shakuntala Devi, shows how simple math can lead to unexpected results. Follow along to find out where the missing Rupee went and learn about the interesting math behind everyday transactions. Can you solve the puzzle?

Puzzle

Two women were selling marbles in the marketplace—one at three for a Rupee and the other at two for a Rupee. One day, both of them had to return home with thirty marbles unsold each. They combined their marbles and handed them to a friend, asking her to sell them at five for 2 Rupees. According to their calculation, selling at 3 for one Rupee and 2 for one Rupee was the same as selling 5 for two Rupees.

They expected to get 25 Rupees for the marbles (10 Rupees for the first woman and 15 Rupees for the second), which is what they would have received if sold separately. However, much to their surprise, they received only 24 Rupees ($60 \times \frac{2}{5}$) for the entire lot.

Now, where did the one Rupee go? Can you explain the mystery?

Solution

There isn’t really any mystery because the explanation is simple. The two ways of selling are identical only when the number of marbles sold at three for a Rupee and two for a Rupee is in the proportion of three to two. Therefore, if the first woman had handed over 36 marbles and the second woman 24 marbles, they would have fetched 24 Rupees, regardless of whether they sold them separately or at five for 2 Rupees.

Since they had the same number of marbles (30 each), this led to a loss of 1 Rupee when combined, in every 60 marbles. So, if they had 60 marbles each, there would be a loss of 2 Rupees, and if there were 90 each (180 altogether), they would lose 3 Rupees, and so on.

In the case of 60 marbles, the missing 1 Rupee arises from the fact that the woman selling 3 marbles per Rupee gains 2 Rupees, and the woman selling 2 marbles per Rupee loses 3 Rupees. The first woman receives 9.5 Rupees, and the second woman receives 14.5 Rupees, so that each loses 0.5 Rupees in the transaction.

About Shakuntala Devi

Shakuntala Devi, known as the “Human Computer,” was a renowned Indian mathematician and writer, celebrated for her extraordinary mental calculation abilities.

Born on November 4, 1929, in Bangalore, India, she demonstrated prodigious talent in arithmetic from a young age. Devi gained global fame by solving complex mathematical problems with lightning speed and without any mechanical aid. Her feats earned her a place in the 1982 edition of The Guinness Book of World Records. Besides her mathematical prowess, she authored numerous books on mathematics, puzzles, and astrology.

Shakuntala Devi’s legacy continues to inspire generations in the fields of mathematics and education.