## Task 6 - 050736

A company was supposed to produce p pieces of the same type of workpiece in 20 working days. By applying better work methods, the workers managed to complete this order 5 working days earlier and produced $k$ more pieces than required.

How many pieces were produced on average each working day beyond the plan?
The number of workpieces to be produced on average each working day according to the plan is $\frac{p}{20}$. In reality, however, $(p+k)$ workpieces were produced in $(20-5)$ days, which means on average $\frac{p+k}{15}$ workpieces per working day.

Therefore, the number of workpieces produced on average each working day in excess of the plan was

$$
\frac{p+k}{15}-\frac{p}{20}=\frac{p+4 k}{60}
$$

Solutions of the third round 1965 adopted from [5]

### 4.8 VI. Olympiad 1966

### 4.8.1 First Round 1966, Class 7