cat 2024 Question 13

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

Accepted Answer

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

Question 13.

Question Explanation