A time study was conducted for a worker in a factory. The observations are as under: 
Observed time 
Output 
Time for which worker could not work 
Performance rating 
40 hours week 
120 units 
20% 
125% 
It was also though appropriate to make the following allowances: 
Fatigue 
Personal needs. 
Unavoidable work delay 
You are required to determine: 
10% 
7% 
3% 
(a) Productive Time; 
(b) Normal Time; and 
(c) Standard Time if above allowances are applied to standard time.

To solve the problem, we need to break it down step by step using the provided data. Here's how we approach each part:

### Given Data:
- **Observed Time**: 40 hours (1 week)
- **Output**: 120 units
- **Time for which worker could not work**: 20%
- **Performance rating**: 125%
- **Allowances**:
  - **Fatigue**: 10%
  - **Personal Needs**: 7%
  - **Unavoidable Work Delay**: 3%

### Step-by-Step Breakdown:

---

### (a) **Productive Time**:
Productive time is the time the worker was actually working, excluding the non-working time. The non-working time is given as 20%.

\[
\text{Productive Time} = \text{Observed Time} \times (1 - \text{Time for which worker could not work})
\]

Substitute the values:

\[
\text{Productive Time} = 40 \, \text{hours} \times (1 - 0.20) = 40 \times 0.80 = 32 \, \text{hours}
\]

---

### (b) **Normal Time**:
Normal time takes into account the worker's performance rating. It is calculated by multiplying the productive time by the performance rating.

\[
\text{Normal Time} = \text{Productive Time} \times \frac{\text{Performance Rating}}{100}
\]

Substitute the values:

\[
\text{Normal Time} = 32 \times \frac{125}{100} = 32 \times 1.25 = 40 \, \text{hours}
\]

---

### (c) **Standard Time**:
Standard time includes allowances, which are a percentage of the standard time. We can calculate it using the formula:

\[
\text{Standard Time} = \frac{\text{Normal Time}}{1 - (\text{Total Allowances})}
\]

Total allowances = Fatigue + Personal Needs + Unavoidable Work Delay

\[
\text{Total Allowances} = 10\% + 7\% + 3\% = 20\%
\]

Now, calculate the standard time:

\[
\text{Standard Time} = \frac{40}{1 - 0.20} = \frac{40}{0.80} = 50 \, \text{hours}
\]

---

### Final Answers:
- (a) **Productive Time**: 32 hours
- (b) **Normal Time**: 40 hours
- (c) **Standard Time**: 50 hours

---

Would you like more details on any of these calculations?

Here are five related questions to consider:
1. How would changing the performance rating affect the standard time?
2. What if the worker could not work for a longer period, say 30% of the time?
3. How do different types of allowances affect standard time calculations?
4. How can productivity be improved based on performance ratings?
5. How would additional fatigue allowances influence overall time management?

**Tip:** Always consider performance rating adjustments when calculating normal time, as it reflects the worker's efficiency.

Learn how to calculate productive time, normal time, and standard time in a time study scenario. Using performance rating, allowances, and observed time, this step-by-step guide provides detailed formulas for calculating each time measure. Perfect for students or professionals interested in time management and efficiency studies.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation