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Explanation:

The initial quantity of rice is x kg.

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

∴ Rice purchased by the first customer = x2+12=x+12
∴ Remaining rice = x-x+12=x-12

Now, the second customer buys half of this, and another half kg.

∴ Rice purchased by the second customer = x-14+12=x+14
∴ Remaining rice = x-12-x+14=x-34

Now, the third customer buys half the remaining rice, and another half kg.

∴ Rice purchased by the third customer = x-38+12=x+18

Since after this purchase, there is no rice left in the store, we conclude that:

x-34-x+18=x-78=0

∴ x = 7

Alternately,
If the shopkeeper had x kg rice before a customer comes, the amount of rice left after every time a customer buys half the amount of rice + half a kg more = x2-12

For 3rd customer.
Now, x2-12 = 0 [No rice is left after third customer]
⇒ x = 1 kg.

Now, the shopkeeper had 1 kg rice when 3rd customer came, hence after 2nd customer left he had 1 kg of rice.

For 2nd customer.
x2-12 = 1
⇒ x = 3 kg.

Now, the shopkeeper had 3 kg rice when 2nd customer came, hence after 1st customer left he had 3 kg of rice.

For 1st customer.
x2-12 = 3
⇒ x = 7 kg.

Now, the shopkeeper had 7 kg rice when 1st customer came.

Hence, option (b).

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