Algebra-10 (CAT-2008)

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)