Ms. Anitha received her salary. She spent half of it shopping and gave Rs. 1…
2023
Ms. Anitha received her salary. She spent half of it shopping and gave Rs. 1 to a beggar. She then spent half of the remaining amount at a hotel and gave Rs. 2 as a tip to the waiter. She then spent half of what remained and gave Rs. 3 as charity. Finally, she was left with Rs. 1. What was her original salary?
- A.
42
- B.
44
- C.
27
- D.
35
Show answer & explanation
Correct answer: A
Concept: When an unknown starting amount goes through a repeated chain of "spend half, then pay a fixed amount" stages, and only the FINAL remaining amount is known, the starting amount can be recovered by reversing the chain stage by stage from the end: undo the fixed payment first (add it back), then undo the halving (double the result). The same chain can equally be written as one linear equation in the unknown and solved forward.
Applying this by working backward from the final Rs. 1, one stage at a time:
Amount left at the very end = Rs. 1.
Undo the charity stage: add back the Rs. 3 charity, then double to undo the half spent before it -> (1 + 3) x 2 = Rs. 8.
Undo the tip stage: add back the Rs. 2 tip, then double -> (8 + 2) x 2 = Rs. 20.
Undo the shopping/beggar stage: add back the Rs. 1 given to the beggar, then double -> (20 + 1) x 2 = Rs. 42.
So Anitha's original salary was Rs. 42.
Cross-check by substituting Rs. 42 forward through all three stages, in the original order:
Shopping: 42/2 = 21 left; after giving Rs. 1 to the beggar: 21 - 1 = 20.
Hotel: 20/2 = 10 left; after the Rs. 2 tip: 10 - 2 = 8.
Spends again: 8/2 = 4 left; after Rs. 3 charity: 4 - 3 = 1, which matches the amount she was left with.
Since the forward substitution reproduces every intermediate amount and the final Rs. 1 exactly, Rs. 42 is confirmed as the original salary.