# Converting Piece Rate into Time Rate

## Concept

This is the reverse of the previous conversion. We are given a per-unit (piece) rate and need to express it as an equivalent hourly/daily rate.

## The Logic (Step-by-Step)

If the worker is paid a fixed amount per unit, and the standard expectation is that a certain number of units come out per hour, then the hourly pay equals the per-unit rate times the standard output per hour.

1. Identify the piece rate — e.g., ₹100 per unit.

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

3. Multiply piece rate by standard units per hour, OR equivalently divide piece rate by standard time per unit (expressed as a fraction of an hour).

## Formula

$$\text{Time Rate (per Hour)} = \frac{\text{Piece Rate Given}}{\text{Standard Time Per Piece (in Hours)}}$$

## Why This Works

We're again re-expressing the same wage on a different denominator. If ₹100 buys 1 unit and 2 units are produced per hour at standard, then 1 hour of standard work costs ₹200.

Worked example

### Example 1

Example 1

AB made 22 units in 10 hours. Piece rate = ₹100 per unit. Standard time per unit = 30 minutes.

Step 1 — Pay on piece-rate basis = 22 × ₹100 = ₹2,200.

Step 2 — Standard time per piece in hours = 30 ÷ 60 = ½ hour.

Step 3 — Time Rate = ₹100 ÷ (½) = ₹200 per hour.

Alternative — Standard units per hour = 2, so Time Rate = ₹100 × 2 = ₹200 per hour. Same answer.

⚠️ Common exam mistakes

Leaving standard time per unit in minutes — the denominator must be in hours (or whichever unit you want the time rate expressed in).
Confusing the conversion direction: piece → time means multiply by standard output per hour, OR divide by standard time per unit (in hours). Don't swap these around.
Using actual time taken instead of standard time per unit.

Reference:

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Conversion of Piece Rate into Time Rate

Worked example

⚠️ Common exam mistakes