Discussion
A shop has some amount of rice. Raman buys half of the rice in the store, plus 1 kg. Nazneen then buys half of the remaining quantity of rice, plus 2 kgs. Amar then buys half of the remaining rice, plus 3 kgs. After this, only 2 kgs of rice are left in the store. How much rice did Raman buy ?
Answer: B
Raman bought 26 kgs.
Work backwards from the 2 kg left at the end. If x kg was in the store before a buyer took half plus k kg, then what remained was x/2 - k.
\[ \begin{aligned} \text{before Amar} &: x/2 - 3 = 2 \Rightarrow x = 10 \\ \text{before Nazneen} &: y/2 - 2 = 10 \Rightarrow y = 24 \\ \text{before Raman} &: z/2 - 1 = 24 \Rightarrow z = 50 \end{aligned} \]
The store began with 50 kg. Raman bought half of it plus 1 kg: 25 + 1 = 26 kg.
50 kgs is the starting stock, not Raman's share; 24 kgs is what was left after Raman's purchase; and 52 kgs comes from doubling 26.
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