Prepare a Departmental Trading Account for departments X, Y, and Z given opening stock and purchases in units, sales units at selling prices (X: 1,020 units at ₹20; Y: 1,920 units at ₹22.50; Z: 2,496 units at ₹25), total purchases value ₹1,00,000, and the same gross profit rate in each department.

What we are trying to find

You are told that all three departments earn the same gross profit (GP) rate, but only the total purchases value (₹1,00,000) is given. So we first find the common GP rate, then compute each department’s cost per unit, and finally prepare the Departmental Trading Account.

Step 1: Compute sales value and closing stock units

Sales value:

• Dept X: $1{,}020 \times 20 = ₹20{,}400$
• Dept Y: $1{,}920 \times 22.50 = ₹43{,}200$
• Dept Z: $2{,}496 \times 25 = ₹62{,}400$

Closing stock units (units available less units sold):

• Dept X: $120 + 1{,}000 - 1{,}020 = 100$ units
• Dept Y: $80 + 2{,}000 - 1{,}920 = 160$ units
• Dept Z: $152 + 2{,}400 - 2{,}496 = 56$ units

Step 2: Use “same GP rate” to relate cost per unit to selling price

Let cost-to-sales ratio be $k$ (same for each department). Then: $$\text{COGS} = k \times \text{Sales}$$ But also, with a constant cost per unit within each department: $$\text{COGS} = (\text{units sold}) \times (\text{cost per unit})$$ So for each department, $$\text{cost per unit} = k \times \text{selling price}$$ Therefore:

• $c_X = 20k$
• $c_Y = 22.5k$
• $c_Z = 25k$

Step 3: Use total purchases value ₹1,00,000 to find $k$

Total purchases value: $$1{,}000c_X + 2{,}000c_Y + 2{,}400c_Z = 100{,}000$$ Substitute $c_X=20k$, $c_Y=22.5k$, $c_Z=25k$: $$1{,}000(20k) + 2{,}000(22.5k) + 2{,}400(25k) = 100{,}000$$ $$20{,}000k + 45{,}000k + 60{,}000k = 100{,}000$$ $$125{,}000k = 100{,}000 \Rightarrow k = 0.8$$ So cost is $80\%$ of sales, and GP is $20\%$ of sales.

Cost per unit:

• Dept X: $c_X = 20 \times 0.8 = ₹16$
• Dept Y: $c_Y = 22.5 \times 0.8 = ₹18$
• Dept Z: $c_Z = 25 \times 0.8 = ₹20$

Step 4: Value opening stock, purchases, closing stock, and compute GP

Purchases (value):

• X: $1{,}000 \times 16 = ₹16{,}000$
• Y: $2{,}000 \times 18 = ₹36{,}000$
• Z: $2{,}400 \times 20 = ₹48{,}000$

Opening stock (value):

• X: $120 \times 16 = ₹1{,}920$
• Y: $80 \times 18 = ₹1{,}440$
• Z: $152 \times 20 = ₹3{,}040$

Closing stock (value):

• X: $100 \times 16 = ₹1{,}600$
• Y: $160 \times 18 = ₹2{,}880$
• Z: $56 \times 20 = ₹1{,}120$

GP (20% of sales):

• X: $0.20 \times 20{,}400 = ₹4{,}080$
• Y: $0.20 \times 43{,}200 = ₹8{,}640$
• Z: $0.20 \times 62{,}400 = ₹12{,}480$

Departmental Trading Account (₹)

(Each department shows GP = 20% of sales, as required.)