Question 5 OR (b)

Departmental Trading Account with a uniform rate of gross profit

8 marks

Time to write: About 16 minutes
Topic: Departmental accounts
Notes: Crux notes

Question

Question 5 OR (b) · 8 marks

Tarangini Ltd carries its business through two departments, about which the relevant information is given here:

Dept.	Purchases (Units)	Opening Stock (Units)	Closing Stock (Units)
A	1,200	120	360
B	2,400	240	480

Additional Information:

The purchases were made at a total cost of Rs. 38,400
The Selling Price per unit for Dept. A and B is, respectively, Rs.10 and Rs. 15.
The rate of gross profit to sales is same for both the departments
For the last two years there is no change in purchase and sale price.

Prepare the departmental trading account.

Reworded from the university paper: names and figures differ, the task is the same. The original paper belongs to the University of Delhi. See DU's question bank.

Before you write

Read off the question and its marks

16 minfor 8 marks

Read from the question

Prepare the departmental trading accountProper formats (heading, date, both sides): post the plain items, then each adjustment, and balance last.

Write it in this order

Workings as you go: each statement feeds the next.

Read the data; tick every adjustment as you plan it 1 min
1 Units sold and sales value for each department 2 marks 4 min
2 Cost per unit derived from the uniform gross-profit condition 3 marks 5 min
3 Departmental Trading Account, both columns 3 marks 5 min
Check: every adjustment used, both sides agree, dates in 1 min

123

Final answer

Check your own figures against these.

Cost per unit A: ₹8
B: ₹12
Uniform gross-profit rate: 20% of sales
Gross profit A: ₹1,920
B: ₹6,480
Total: ₹8,400; The rate holds department by department: 1,920 ÷ 9,600 and 6,480 ÷ 32,400 are both exactly 20%

Try it first. About 16 minutes for 8 marks. Write it out, then open the solution and check your figures against the final answer.

Solution

Hover or tap a marked figure, like 72,000, to see how it is made and where else it appears.

The one derivation the question turns on

Only the combined purchase cost is given, so neither department's cost per unit is known. Condition

supplies the missing equation. If gross profit is the same fraction of sales in both departments, then cost must be the same fraction of selling price in both:

cost per unit ÷ selling price per unit is identical for A and B

so B's unit cost is A's scaled by the ratio of the two selling prices, ₹15 ÷ ₹10:

Step	Working	Result
Express B's unit cost in terms of A's	cost B = cost A × 15 ÷ 10	1.5 × cost A
Substitute into the combined purchase cost	1,200 × cost A + 2,400 × 1.5 × cost A = 38,400	4,800 × cost A = 38,400
Cost per unit: Department A	38,400 ÷ 4,800	₹8
Cost per unit: Department B	8 × 1.5	₹12
Uniform rate of gross profit to sales	1 − 8 ÷ 10 = 1 − 12 ÷ 15	20%

The rate is confirmed independently below: each department's gross profit comes out at exactly 20% of its own sales, and the two unit costs rebuild the ₹38,400 combined purchase cost.

Conventions committed to

Departmental accounts exist so that the result of each part of the business can be seen separately rather than only the result of the whole, and under the joint-accounts method a single Trading and Profit & Loss Account is prepared with a column per department to disclose each department's result. Two readings follow.

Every stock layer carries the same unit cost. Note (iv) says prices have not changed for two years, so opening stock, purchases and closing stock are all valued at the department's single derived cost per unit. Without note (iv) the opening stock could carry an older cost and the problem would be indeterminate: which is why the paper supplies it.
Only a Trading Account is asked for, so its debit side takes opening stock and purchases and its credit side sales and closing stock, and no Profit & Loss section is prepared: the question gives no expenses to carry into one.
The two columns are kept side by side because the comparison is the point. Setting each department's result against the other is itself one of the stated benefits of departmental accounting: comparison of departmental results is what lets performance be judged and a competitive spirit be developed between them. Here that comparison is unusually pointed: because the gross-profit rate is identical by assumption, the columns differ only in volume and price, so B's ₹6,480 of gross profit against A's ₹1,920 is entirely a matter of scale, not of trading efficiency.

Working notes

WN1Units sold and sales value

	Dept. A	Dept. B
Opening stock (units)	120	240
Add: purchases (units)	1,200	2,400
Less: closing stock (units)	360	480
Units sold	960	2,160
Selling price per unit ₹	10	15
Sales ₹	9,600	32,400

WN2Money values at the derived unit costs

	Dept. A @ ₹8	Dept. B @ ₹12
Opening stock ₹	960	2,880
Purchases ₹	9,600	28,800
Closing stock ₹	2,880	5,760

Purchases rebuild the given combined cost: 9,600 + 28,800 = ₹38,400 ✓

Departmental Trading Account

Debit (each column foots ✓)

Particulars	Dept. A ₹	Dept. B ₹	Total ₹
To Opening Stock	960	2,880	3,840
To Purchases	9,600	28,800	38,400
To Gross Profit c/d	1,920	6,480	8,400
	12,480	38,160	50,640

Credit

Particulars	Dept. A ₹	Dept. B ₹	Total ₹
By Sales	9,600	32,400	42,000
By Closing Stock	2,880	5,760	8,640
	12,480	38,160	50,640

Result: Cost per unit A ₹8 · B ₹12 · uniform gross-profit rate 20% of sales · gross profit A ₹1,920 · B ₹6,480 · total ₹8,400. The rate holds department by department: 1,920 ÷ 9,600 and 6,480 ÷ 32,400 are both exactly 20%.

Where the 8 marks sit

#	Component	Marks
1	Units sold and sales value for each department	2
2	Cost per unit derived from the uniform gross-profit condition (₹8 and ₹12)	3
3	Departmental Trading Account, both columns (→ gross profit 8,400)	3
	Total	8

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