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. \(2 \le x \le 6\)
• B. \(5 \le x \le 8\)
• C. \(9 \le x \le 12\)
• D. \(11 \le x \le 14\)
• E. \(13 \le x \le 18\)

Hint:

When quantities reduce in fractions with extra fixed amounts, work backwards from the end to the start for faster calculation.

Answer 1

The Correct Option is B

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 \(\boxed{5 \le x \le 8}\).