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Puzzle | How much he had initially?

  • Difficulty Level : Basic
  • Last Updated : 16 Dec, 2019
Geek Week

Puzzle: Rama started on a quest of visiting temples, with few coins in his pockets. As soon as he visits any temple, the money in his pocket gets doubled and on his way out, he donates Rs. 100 to each temple. He visits 4 temples on his quest. After visiting the last temple, his pocket is empty of all the money, so how much money he had initially.

Solution: Let’s assume Rama began his quest with Rs. x.

1st Temple: As soon as he enters the temple, his money is doubled to 2x. On his way out he donates Rs. 100. Therefore, he is left with Rs. Rs. (2x – 100).

2nd Temple: As soon as he enters the temple, his money is doubled to 2(2x – 100). On his way out he donates another Rs. 100 and he is left out with Rs. (4x – 300)

3rd Temple: As soon as he enters the temple, his money is doubled to 2(4x – 300). On his way out he donates another Rs. 100 and he is left with Rs. (8x – 700)

4th Temple: As soon as he enters the temple, his money is doubled to 2(8x – 700). On his way out he donates another Rs. 100 and he is left with Rs. (16x – 1500).

According to the question, after his last visit, he completely runs out of money.

Therefore,
=> 16x - 1500 = 0;
=> x = 1500/16;
=> x = 93.75

Rama had started his quest with Rs 93.75 in his pocket.

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