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CAT 2008 | Question: 09

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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. There after no rice left in the shop. Which of the following best describes the value of $x?$

  1. $2 \leq x \leq 6$

  2. $5 \leq x \leq 8$

  3. $9 \leq x \leq 12$

  4. $11 \leq x \leq 14$

  5. $13 \leq x \leq 18$

1 Answer

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A shop stores x kg of rice.

Rice purchased by first customer = $\frac{x}{2}+\frac{1}{2} = \frac{x+1}{2}$kg

Remaining amount of rice = $x - \frac{x+1}{2}$ =$\frac{x-1}{2}$kg

Rice purchased by Second customer =$\frac{x-1}{4}+\frac{1}{2}=\frac{x+1}{4}$kg

Remaining amount of rice=$\frac{x-1}{2}+\frac{x-1}{4}=\frac{x-3}{4}$kg

Rice purchased by Third customer = $\frac{x-3}{8}+\frac{1}{2}=\frac{x+1}{8}$kg

After rice purchased by Third customer there after no rice left in the shop.

Here,total amount of rice should be equal to the Total amount of rice purchased by all customers.

 

$x= \frac{x+1}{2} + \frac{x+1}{4} + \frac{x+1}{8}$

$8x=7x+7$

x=7

 

Hence,Option (2) 5 ≤ x ≤ 8 is the correct choice. 

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