Latest CAT Aptitude Question SOLUTION: A shop stores some 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

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(#M40009702) CAT Logical Reasoning question Keep an EYE

A shop stores some 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.What was the initial quantity of rice (kg) stored in the shop?

Asked In CAT Devendra Marghade (11 years ago)

Solved Aman Read Solution (4)

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Aman  (11 years ago)

In such cases,
if there are n customers, then
initial quantity =(2^n)-1
in this case, initial quantity = 2^3-1=7 kg
which is taken as 4 ,2,1 kg by 3 customers.

Is this solution Helpfull? Yes (8) | No (3)  

arti nigam  (11 years ago)

7kg..assume the rice be x kg.. first customer buys half of x plus 1/2kg rice i.e x/2+1/2.. rice left is x/2-1/2.. 2nd customer buys half the remaining amt plus1/2kg of rice i.e 1/2(x/2-1/2)+1/2.. rice left is x/4-3/4.. 3rd customer also does same buys 1/2(x/4-3/4)+1/2.. rice left is x/8-7/8..
nw no rice is left.. therefore x/8-7/8=0..
hence x=7..

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suganya  (11 years ago)

let d initial amt of rice 'x'
then 1st customer buys (x+1)/2kg then remaining amt of rice will be (x-1)/2kg
2nd customer buys(x+1)/4kg then remaining will be (x-3)/4kg
3rd customer buys (x+1)/8kg then remaining will be zero
therefore (x-3)/4-(x+1)/8=0
so x=7

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hemant  (9 years ago)

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

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