CAT 2024 Slot 1 QA Question & Solution
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
Options
Solution
Let us say the quantity of grains is X
For the first customer he sells $\frac{X}{2}+3$
Remaining is $\frac{X}{2}-3$
Second customer he sells: $\frac{X}{4}-\frac{3}{2}+3=\frac{X}{4}+\frac{3}{2}$
Remaining will be $\frac{X}{4}-\frac{9}{2}$
Third customer he sells: $\frac{X}{8}-\frac{9}{4}+3$ = $\frac{X}{8}+\frac{3}{4}$
Remaining will be $\frac{X}{8}-\frac{21}{4}$
Now, this is said to be 0,
$\frac{X}{8}-\frac{21}{4}=0$
X=42