Question

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

• A. 42
• B. 18
• C. 36
• D. 50

Answer 1

Answer: (A)

42

Answer 2

Let the initial quantity of grains be $x$. The first customer buys half of $x$ plus 3 kg, leaving $\frac{x}{2} - 3$ kg. The second customer then buys half of the remaining grains plus 3 kg, leaving $\frac{x}{4} - 3$ kg. The third customer buys half of what is left plus 3 kg, leaving 0 grains. Thus, we have the equation:

$\frac{x}{8} - 3 = 0 \implies x = 42$