Question:
A shop stores \(x\) kg of rice. The first customer buys half this amount plus half a kg of rice. The second customer buys half the remaining amount plus half a kg of rice. Then the third customer also buys half the remaining amount plus half a kg of rice. Thereafter, no rice is left in the shop. Which of the following best describes the value of \(x\)?
A shop stores \(x\) kg of rice. The first customer buys half this amount plus half a kg of rice. The second customer buys half the remaining amount plus half a kg of rice. Then the third customer also buys half the remaining amount plus half a kg of rice. Thereafter, no rice is left in the shop. Which of the following best describes the value of \(x\)?
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When quantities reduce in fractions with extra fixed amounts, work backwards from the end to the start for faster calculation.
Updated On: Mar 24, 2026
- \(2 \le x \le 6\)
- \(5 \le x \le 8\)
- \(9 \le x \le 12\)
- \(11 \le x \le 14\)
- \(13 \le x \le 18\)
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The Correct Option is B
Solution and Explanation
Let the initial quantity be \(x\) kg.
After the first customer: Remaining = \(\frac{x}{2} - 0.5\) kg.
After the second: Remaining = \(\frac{\frac{x}{2} - 0.5}{2} - 0.5 = \frac{x}{4} - 0.75\) kg.
After the third: Remaining = \(\frac{\frac{x}{4} - 0.75}{2} - 0.5 = \frac{x}{8} - 0.875\) kg.
Since no rice is left:
\[
\frac{x}{8} - 0.875 = 0
\]
\[
\frac{x}{8} = 0.875
\]
\[
x = 7
\]
Thus, the correct range is \(\boxed{5 \le x \le 8}\).
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