CAT 2024Slot 1QAQuestion & 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
50
36
42
18
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