Question:
The owner of a local jewellery store hired three watchmen to guard his diamonds, but a thief still got in and stole some diamonds. On the way out, the thief met each watchman, one at a time. To each he gave \( \frac{1}{2} \) of the diamonds he had then, and 2 more besides. He escaped with one diamond. How many did he steal originally?
The owner of a local jewellery store hired three watchmen to guard his diamonds, but a thief still got in and stole some diamonds. On the way out, the thief met each watchman, one at a time. To each he gave \( \frac{1}{2} \) of the diamonds he had then, and 2 more besides. He escaped with one diamond. How many did he steal originally?
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In problems involving halving and giving away, use recursive relations to simplify the calculations.
Updated On: Aug 4, 2025
- 40
- 36
- 25
- None of these
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The Correct Option is C
Solution and Explanation
Let the original number of diamonds be \( x \). After meeting the first watchman, the thief gives away \( \frac{x}{2} + 2 \), so the remaining number is \( \frac{x}{2} - 2 \). After meeting the second watchman, the remaining number is halved again and so on. After the last meeting, he has one diamond left. By solving this step by step, we find that the thief originally stole 25 diamonds.
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