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? (CAT 2008) (1) 2 ≤ x ≤ 6 (2) 5 ≤ x ≤ 8 (3) 9 ≤ x ≤ 12 (4) 11≤ x ≤ 14 (5) 13 ≤ x ≤ 18

Answer 1

the answer is option (4) because value of x is 11. 

Answer 2

Step-by-step explanation:

Initial quantity of the rice = x

The first customer buys half the total rice and another half kg.

Rice purchased by first customer = x/2 + 1/2 = (x + 1)/2

So, rice left after the first customer = x - (x + 1)/2 = (x - 1)/2

Now the second customer buys half the left rice and another half kg.

Rice purchased by second customer = (x - 1)/4 + 1/2 = (x + 1)/4

So, rice left after the second customer = (x - 1)/2 - (x + 1)/4 = (x - 3)/4

Now the third customer buys half the left rice and another half kg.

Rice purchased by third customer = (x - 3)/8 + 1/2 = (x + 1)/8

So, rice left after the second customer = (x - 3)/4 - (x + 1)/8 = (x - 7)/8

Given that (x - 7)/8 = 0 => x = 7