Cost price, selling price, profit and loss

Learning outcome

Distinguish cost from sales receipts, include stated overheads, and calculate profit, loss or the selling price needed to break even.

Meaning and method

Cost price (CP) is the amount invested in the item under the problem’s assumptions. Selling price (SP) is the amount actually received from selling it. Neither term automatically tells you whether the transaction succeeds.

For these problems, include stated transport, repair, packing or other overhead expenses in cost. Ignore taxes and unstated charges. When an expense belongs to a whole batch, include it once in the batch cost; divide it equally only when equal allocation is appropriate.

Profit = SP - CP when SP is greater than CP.

Loss = CP - SP when CP is greater than SP.

When SP = CP, the transaction breaks even: neither profit nor loss occurs. We report a loss as a positive amount and label it “loss,” rather than leaving an unexplained negative answer.

Why subtract? Sales receipts first recover the investment. Anything left is profit; any unrecovered part is loss. Always compare matching quantities: one item’s selling price with its cost, or the whole batch’s receipts with its total cost. Assume every item counted as sold is actually sold.

Worked examples

Example 1 — A direct sale. An organiser costs ₹735 and sells for ₹812. Profit = 812 - 735 = ₹77. Check: cost plus profit is 735 + 77 = ₹812.

Example 2 — Include overheads. A stand costs ₹1,280; packing costs ₹45 and transport ₹75. Effective CP = 1280 + 45 + 75 = ₹1,400. Selling it for ₹1,336 produces a loss of 1400 - 1336 = ₹64. Comparing receipts with the purchase price alone would give the wrong conclusion.

Example 3 — A complete batch. A seller buys 24 flasks at ₹215 each and pays ₹288 delivery, allocated equally. Total CP = 24 × 215 + 288 = ₹5,448; unit CP = 5448 ÷ 24 = ₹227. All sell at ₹245 each, giving receipts of 24 × 245 = ₹5,880. Total profit = 5880 - 5448 = ₹432, also 24 × (245 - 227).

Common mistakes

Do not count a batch expense once per item. Do not compare total cost with a single item’s price. Selling above the purchase price does not guarantee profit: receipts must also cover stated overheads.

Practice questions

1. An organiser costs ₹568 and sells for ₹649. Find the profit or loss.
2. A lamp costs ₹940, with ₹85 repairs and ₹35 transport. It sells for ₹1,018. Find the effective cost and result.
3. Eighteen lunchboxes cost ₹146 each, with ₹144 total packing. All sell for ₹169 each. Find the total profit.
4. Sixteen stools cost ₹375 each, plus ₹480 total delivery. Ten sell at ₹420 each. With no further costs, what equal price for each remaining stool makes the batch break even?

Worked answers

1. SP exceeds CP, so profit = 649 - 568 = ₹81.
2. Effective CP = 940 + 85 + 35 = ₹1,060. Loss = 1060 - 1018 = ₹42.
3. Total CP = 18 × 146 + 144 = ₹2,772. Receipts = 18 × 169 = ₹3,042. Profit = 3042 - 2772 = ₹270.
4. Total CP = 16 × 375 + 480 = ₹6,480. Earlier receipts = 10 × 420 = ₹4,200. The remaining 6 stools must recover 6480 - 4200 = ₹2,280, so each must sell for 2280 ÷ 6 = ₹380.