Question

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?

Answer 1

38.25 kg

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.
`x=(25.5)/(0.17)` i.e. x = 250

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