Question

A time study was carried out for a job broken into two elements. For each element, three iterations of task were observed, and observed time was recorded. The observed times (in seconds) and the rating factor for each element are given in the table.

Work element	Observed time (seconds)	Rating factor
A	20; 25; 21	105%
B	19; 17; 18	90%

If a further 20% needs to be added for allowances, then the standard output of the worker is ______ units per hour (in integer).

Hint:

Find normal time for each element, add allowance, then convert standard time per unit into units produced per hour.

Answer 1

Correct Answer: 76

Step 1: Understanding the Concept:
A job is made of two elements, A and B, each timed three times using a stopwatch.
We must convert these raw observed times into a standard time per job, and then convert that standard time into an hourly production rate.

Step 2: Key Formula or Approach:
Average Observed Time = sum of readings divided by number of readings.
Normal Time = Average Observed Time \( \times \) Rating Factor.
Standard Time (per element) = Normal Time \( \times (1 + \text{Allowance Fraction}) \), and since allowance is a common percentage add-on, we can apply it to each element individually and then add the two standard times together to get the standard time for the whole job.

Step 3: Detailed Explanation:
Element A:
\[ \text{Average OT}_A = \frac{20 + 25 + 21}{3} = \frac{66}{3} = 22 \text{ s} \]
\[ NT_A = 22 \times 1.05 = 23.1 \text{ s} \]
\[ ST_A = 23.1 \times 1.20 = 27.72 \text{ s} \]
Element B:
\[ \text{Average OT}_B = \frac{19 + 17 + 18}{3} = \frac{54}{3} = 18 \text{ s} \]
\[ NT_B = 18 \times 0.90 = 16.2 \text{ s} \]
\[ ST_B = 16.2 \times 1.20 = 19.44 \text{ s} \]
Adding the standard times of the two elements gives the standard time for one complete job:
\[ ST = 27.72 + 19.44 = 47.16 \text{ s/unit} \]
Now convert this to an hourly rate using the 3600 seconds available in one hour:
\[ \text{Output per hour} = \frac{3600}{47.16} = 76.34 \text{ units} \]

Final Answer:
Since the worker cannot complete a fractional unit within the hour, the standard output rounds down to the nearest whole unit. \[ \boxed{76 \text{ units per hour}} \]