During one week the workman x manufactured 200 units.He recived wages for a guaranteed 44 hours week at the rate of Rs. 15 per hour .THE time allowed to produce one unit is 18 minutes . Calculate his gross wages under each of the following methods of remunerating labour :

(a) Time rate
(b) Piece rate with guaranteed weekly wages
(c) Halsey premium plan ,50% bonus
(d) Rowan premium plan

We need to calculate earning per hour under bonus scheme

Therefore standard hour for the production will be 200 x 18 / 60
= 60 hours.
Now original hour is 45 hours.
Therefore Earnings will be = hours worked x rate per hour + ½ (standard hour – original hour) x Rate per hour
= 45 x Rs 1.80 + ½ (60 – 45) x 1.80
= Rs 81 + Rs 13.50
= Rs 94.50
Therefore earnings per hour is Rs 94.50 / 45
= Rs 2.10 per hour.
Now under Rowan Bonus Scheme
Earnings = Original hour x Rate per hour + Original hour / standard hour x (standard hour - Original hour ) x R
= 45 x Rs 1.80 + 45 / 60 x (60 – 45) x Rs 1.80
= Rs 81 + Rs 20.25
= Rs 101.25
Earnings per hour = Rs 101.25 / 45 hours
= Rs 2.25 per hour.

To calculate the workman's gross wages under each method of remunerating labor, we need to consider the number of hours worked and the number of units produced. Let's calculate the gross wages under each method:

(a) Time Rate Method:
The workman is guaranteed to work 44 hours per week, and he is paid at a rate of Rs. 15 per hour.

Gross wages = Number of hours worked * Hourly rate
Gross wages = 44 hours * Rs. 15 per hour
Gross wages = Rs. 660

(b) Piece Rate Method with Guaranteed Weekly Wages:
The workman manufactured 200 units in one week. The time allowed to produce one unit is 18 minutes. We need to calculate the number of hours he worked.

Number of hours worked = (Number of units * Time allowed per unit) / 60
Number of hours worked = (200 * 18) / 60
Number of hours worked = 60 hours

Now, let's calculate the piece rate wages:

Piece rate wages = Number of units * Piece rate
Piece rate wages = 200 units * Rs. 15 per unit
Piece rate wages = Rs. 3000

Since the piece rate wages are less than the guaranteed weekly wages (Rs. 660), the workman will receive the guaranteed weekly wages of Rs. 660.

(c) Halsey Premium Plan with 50% Bonus:
Under the Halsey Premium Plan, the workman will receive the guaranteed weekly wages plus a 50% bonus based on the time saved.

Time allowed to produce 200 units = Number of units * Time allowed per unit
Time allowed to produce 200 units = 200 units * 18 minutes
Time allowed to produce 200 units = 3600 minutes

Time saved = Time allowed to produce 200 units - Actual time taken to produce 200 units
Time saved = 3600 minutes - (Number of hours worked * 60 minutes)
Time saved = 3600 minutes - (60 hours * 60 minutes/hour)
Time saved = 3600 minutes - 3600 minutes
Time saved = 0 minutes

Bonus = (50% of Time saved) * Hourly rate
Bonus = (0.5 * 0 minutes) * Rs. 15 per hour
Bonus = Rs. 0

Gross wages = Guaranteed weekly wages + Bonus
Gross wages = Rs. 660 + Rs. 0
Gross wages = Rs. 660

The workman's gross wages under the Halsey Premium Plan with a 50% bonus will be Rs. 660.

(d) Rowan Premium Plan:
Under the Rowan Premium Plan, the workman will receive the guaranteed weekly wages plus a bonus based on the time saved as a percentage of the time allowed.

Time allowed to produce 200 units = Number of units * Time allowed per unit
Time allowed to produce 200 units = 200 units * 18 minutes
Time allowed to produce 200 units = 3600 minutes

Time taken to produce 200 units = Number of hours worked * 60 minutes
Time taken to produce 200 units = 60 hours * 60 minutes/hour
Time taken to produce 200 units = 3600 minutes

Time saved = Time allowed to produce 200 units - Actual time taken to produce 200 units
Time saved = 3600 minutes - 3600 minutes
Time saved = 0 minutes

Percentage of time saved = (Time saved / Time allowed to produce 200 units) * 100
Percentage of time saved = (0 minutes / 3600 minutes) * 100
Percentage of time saved = 0%

Bonus = (Percentage of time saved / 100) * Guaranteed weekly wages
Bonus = (0% / 100) * Rs. 660
Bonus = Rs. 0

Gross wages = Guaranteed weekly wages + Bonus
Gross wages = Rs. 660 + Rs. 0
Gross wages = Rs. 660

The workman's gross wages under the Rowan Premium Plan will be Rs. 660.

To calculate the gross wages under each method of remunerating labor, we need to calculate the total hours worked and the total number of units produced during the week.

First, let's calculate the total hours worked:

(a) Time rate:
The workman x has a guaranteed 44 hours per week. Therefore, the total hours worked under the time rate method is 44 hours.

(b) Piece rate with guaranteed weekly wages:
Since the workman x manufactured 200 units in one week, and the time allowed to produce one unit is 18 minutes, we can calculate the total hours worked as follows:
Total hours worked = Total units produced * Time allowed per unit / 60 minutes per hour
Total hours worked = 200 * 18 / 60 = 60 hours

(c) Halsey premium plan, 50% bonus:
Under the Halsey premium plan, the workman x would still receive the guaranteed 44 hours of wages. We need to calculate the additional bonus hours based on the time saved in producing the units.
Time saved per unit = Standard time per unit - Time allowed per unit
Time saved per unit = 60 minutes - 18 minutes = 42 minutes

Total bonus hours = Total units produced * Time saved per unit / 60 minutes per hour
Total bonus hours = 200 * 42 / 60 = 140 hours

Total hours worked = Guaranteed hours + Bonus hours
Total hours worked = 44 hours + 140 hours = 184 hours

(d) Rowan premium plan:
Under the Rowan premium plan, the workman x would still receive the guaranteed 44 hours of wages. We need to calculate the additional bonus hours based on the proportion of time saved in producing the units.

Time saved per unit = Standard time per unit - Time allowed per unit
Time saved per unit = 60 minutes - 18 minutes = 42 minutes

Total time saved = Total units produced * Time saved per unit
Total time saved = 200 * 42 = 8400 minutes

Efficiency = Actual time taken / Standard time taken
Efficiency = Total time taken / (Total units produced * Time allowed per unit) = (44 hours * 60 minutes per hour) / (200 * 18 minutes per unit)

Bonus hours = Efficiency * Total time saved / 60 minutes per hour
Bonus hours = Efficiency * 8400 / 60 = (44 * 60 * 8400) / (200 * 18 * 60)

Total hours worked = Guaranteed hours + Bonus hours
Total hours worked = 44 hours + Bonus hours

Now, we can calculate the gross wages under each method:

(a) Time rate:
Gross wages = Total hours worked * Rate per hour
Gross wages = 44 hours * Rs. 15 per hour

(b) Piece rate with guaranteed weekly wages:
Gross wages = Total hours worked * Rate per hour
Gross wages = 60 hours * Rs. 15 per hour

(c) Halsey premium plan, 50% bonus:
Gross wages = Total hours worked * Rate per hour + Bonus hours * Rate per hour * (50% premium)
Gross wages = 184 hours * Rs. 15 per hour + 140 hours * Rs. 15 per hour * (50/100)

(d) Rowan premium plan:
Gross wages = (Guaranteed hours + Bonus hours) * Rate per hour
Gross wages = (44 hours + Bonus hours) * Rs. 15 per hour

Now you can calculate the gross wages for each method of remunerating labor using the formulas provided.