During the first hour of operation the farm stand owner sold 15% of the apples he had. on the second hour he sold 20% of the remaining apples. on the third hour he sold 25% of the remaining apples, and so on, selling 5% more each following hour. if during the second hour 25.5 kg of apples were sold, how many kilograms of apples will be sold during the fourth hour of operation?

38.25 kg

Step-by-step explanation:

Let the number of apples sold = x

Now, on the first hour he sold 15% of the apples i.e. he sold 0.15x kg of apples.

So, the remaining apples = x - 0.15x = 0.85x

Further, on the second hour he sold 20% of the remaining apples i.e. he sold 0.20 × 0.85x = 0.17x kg of apples.

Thus, the remaining apples = 0.85x - 0.17x = 0.68x

Then, on the third hour he sold 25% of the remaining apples i.e. he sold 0.25 × 0.68x = 0.17x kg of apples.

So, the remaining apples = 0.68x - 0.17x = 0.51x

Moreover, on the fourth hour he will sell 30% ( i.e. 5% more of 25% ) of the remaining apples i.e. he sold 0.30 × 0.51x = 0.153x kg of apples.

As, during the second hour, he sold 25.5 kg of apples.

Then, 0.17x = 25.5 i.e. i.e. x = 250

Hence, during the fourth hour, he will sell 0.153x = 0.153 × 250 = 38.25 kg of apples.