A shop wants to sell a certain quantity (in kg) of grains. It sells half the quantity and an additional 3 kg of these grains to the first customer. Then, it sells half of the remaining quantity and an additional 3 kg of these grains to the second customer. Finally, when the shop sells half of the remaining quantity and an additional 3 kg of these grains to the third customer, there are no grains left. The initial quantity, in kg, of grains is

✅ Correct Option: 1

What We Know	Mathematical Expression
Shop starts with some quantity	Let's call this $x$ kg
Shop sells "half + 3 kg"	Amount sold $= \frac{x}{2} + 3$ kg
What's left after selling	Amount left $= x - (\frac{x}{2} + 3)$
Simplify the "Amount left"	$=\boxed{ \frac{x}{2} - 3}$ kg

Hence, we have $\frac{x}{2}-3$ left after selling to each customer.

We can think in reverse (as no grains are left after selling to the 3rd customer):

Step	Left After Sale	$\frac{x}{2} - 3 =$ Left After Sale	Solution	Before Sale
After 3rd	0 kg	$\frac{x}{2} - 3 = 0$	$x = 6$	6 kg before 3rd customer
After 2nd	6 kg	$\frac{x}{2} - 3 = 6$	$x = 18$	18 kg before 2nd customer
After 1st	18 kg	$\frac{x}{2} - 3 = 18$	$x = 42$	42 kg initially

Hence, there were 42 kgs.

You could also try with options (could be faster):

Trying with $x = 42$ kg:

Customer	Quantity at Start	Total Sold = Half Quantity + 3 kg	Remaining
Initial	42 kg	-	42 kg
Customer 1	42 kg	21 + 3 = 24 kg	18 kg
Customer 2	18 kg	9 + 3 = 12 kg	6 kg
Customer 3	6 kg	3 + 3 = 6 kg	0 kg ✓

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