# Converting Time Rate into Piece Rate

## Concept

Sometimes a question gives us an hourly/daily wage rate but asks us to think in terms of per-unit (piece) rate. We need a logical bridge between time-based pay and output-based pay.

## The Logic (Step-by-Step)

If the firm pays a fixed amount per hour, and the worker is expected (by standard) to produce a fixed number of units in that hour, then the per-unit pay is simply the hourly pay divided by the standard output per hour.

1. Identify the hourly rate — e.g., ₹200 per hour.

2. Identify the standard time per unit — e.g., 30 minutes per unit.

3. Derive standard output per hour = 60 ÷ (standard time per unit in minutes) = 60 ÷ 30 = 2 units/hour.

4. Divide the hourly rate by standard output per hour to get the piece rate.

## Formula

$$\text{Piece Rate} = \frac{\text{Rate per Hour (or per Day)}}{\text{Standard units produced in 1 Hour (or 1 Day)}}$$

## Why This Works

We are simply re-expressing the same wage on a different denominator. If ₹200 buys the firm 1 hour of work, and 1 hour is supposed to produce 2 units, then each unit effectively costs ₹100 in wages. The total wage bill doesn't change — only the way we describe it.

Worked example

### Example 1

Example 1

AB made 22 units in 10 hours. Hourly rate = ₹200/hour. Standard time per unit = 30 minutes.

Step 1 — Pay on hourly basis = 10 × ₹200 = ₹2,000.

Step 2 — Standard output per hour = 60 ÷ 30 = 2 units/hour.

Step 3 — Piece Rate = ₹200 ÷ 2 = ₹100 per unit.

Check — At ₹100 × 22 units actually produced = ₹2,200 (this is the worker's piece-rate earning, not the time-rate cost). The conversion has correctly translated the time rate into an equivalent piece rate.

⚠️ Common exam mistakes

Forgetting to convert standard time per unit from minutes to hours before computing units per hour.
Multiplying instead of dividing — students sometimes compute Rate × Units instead of Rate ÷ Units.
Using actual units produced instead of standard units per hour in the denominator. The piece rate is benchmarked to standard performance, not actual.

Reference:

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Conversion of Time Rate into Piece Rate

Worked example

⚠️ Common exam mistakes