Two girls went shopping. In the first shop, they spent half of what they had…
2024
Two girls went shopping. In the first shop, they spent half of what they had plus ₹2. In the second shop, they spent half of the remaining amount plus ₹5. In the third shop, they spent half of what then remained. The ₹5 that was left was spent on coffee. How much money did they start with?
- A.
64
- B.
56
- C.
60
- D.
52
Show answer & explanation
Correct answer: A
Concept: when an amount goes through repeated "spend half plus a fixed sum" steps, the fastest way to recover the starting amount is to work backward from the known final remainder, undoing each step in reverse order (last shop first): to undo "spend half plus a fixed amount", add that fixed amount back to the leftover, then double it.
After the third shop, ₹5 remained (this was then spent on coffee). Since the third shop's spend was exactly half of what remained (no fixed amount added there), the amount just before the third shop was double this leftover: 5 × 2 = ₹10.
The ₹10 before the third shop is what was left after the second shop. Before the second shop, they spent half of what they had plus ₹5, so to undo it: add the ₹5 back to the ₹10, then double: (10 + 5) × 2 = ₹30. So ₹30 was left after the first shop.
The ₹30 after the first shop is what remained once they'd spent half of the starting amount plus ₹2. To undo it: add the ₹2 back to the ₹30, then double: (30 + 2) × 2 = ₹64. This is the amount they started with.
Cross-check (forward): starting with ₹64 — Shop 1: spend 64/2 + 2 = ₹34, leaving ₹30. Shop 2: spend 30/2 + 5 = ₹20, leaving ₹10. Shop 3: spend 10/2 = ₹5, leaving exactly ₹5 for coffee. This matches the problem exactly.
So the girls started with ₹64.