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?
(1)2 ≤ x ≤ 6 (2)5 ≤ x ≤ 8 (3)9 ≤ x ≤ 12 (4)11 ≤ x ≤ 14 (5) 13 ≤ x ≤ 18
Solution follows here:
Solution:
Following
table gives information about taken out/ left out quantities, one
after another transaction:
Taken out

Left out


x/2 + 1/2

x/2  1/2

taken by first
customer

x/4  1/4 + 1/2

x/4  3/4

taken by first
customer

x/8 3/8 +1/2

x/8 3/8  1/2

taken by first
customer

It is
given that no rice left after third iteration,
Hence x/8
– 3/8 – ½ = 0 => x = 7
The best
answer out of the given options for x=7 is (2)
Answer
(2)
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