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State Board · Class 6 · Mathematics

Lesson 12: Profit and Loss

5 concepts · 40 practice questions with answers · Free to read

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Cost price, selling price, profit and loss

From daily life

A vendor buys mangoes in the wholesale market and sells them in the street. If he sells for more than he paid, he earns. If he sells for less, he loses. Trade is built on these two prices.

Simple definition

The price at which goods are bought is the cost price (CP, खरेदी किंमत). The price at which they are sold is the selling price (SP, विक्री किंमत). If SP is more than CP there is a profit (नफा); if SP is less than CP there is a loss (तोटा).

Rule 1: CP, SP, profit and loss — SP > CP means profit, SP < CP means loss, and SP = CP means no profit and no loss.

Profit when SP is more than CP; loss when SP is less.PROFITCP50SP78SP > CPProfit = SP − CPLOSSCP78SP50SP < CPLoss = CP − SP

In the figure : In the figure profit when SP > CP, loss when SP < CP.

  • Easy : Easy: CP ₹ 50 and SP ₹ 70: SP is more, so there is a profit.
  • Medium : Medium: CP ₹ 90 and SP ₹ 75: SP is less, so there is a loss.
  • Exam-type : Exam: CP ₹ 120 and SP ₹ 120 give neither profit nor loss.

Rule 2: Profit and loss amounts — Profit = SP − CP and Loss = CP − SP. Seema bought books for ₹ 800 and sold them for ₹ 950, so her profit is 950 − 800 = ₹ 150.

Cost ₹1,250, selling ₹1,560: profit ₹310.Cost price₹ 1,250Selling price₹ 1,250310Profit1,560 − 1,250 = 310Selling price is more, so there is a profit

In the figure : In the figure cost ₹ 1,250 and selling ₹ 1,560: profit ₹ 310.

  • Easy : Easy: CP ₹ 200 and SP ₹ 260: profit = 260 − 200 = ₹ 60.
  • Medium : Medium: CP ₹ 640 and SP ₹ 580: loss = 640 − 580 = ₹ 60.
  • Exam-type : Exam: Bought for ₹ 1,800 and sold for ₹ 2,150: profit = 2,150 − 1,800 = ₹ 350.
Remember

Profit: SP > CP. Loss: SP < CP. Profit = SP − CP. Loss = CP − SP.

Common mistake

Subtracting in the wrong order. Always subtract the smaller from the larger.

Shortcut

Memory clue: "विक्री जास्त = नफा; विक्री कमी = तोटा".

Spot the difference

CaseResult
SP > CPProfit = SP − CP
SP < CPLoss = CP − SP
SP = CPNo profit, no loss

Practice questions

Easy
  1. 1CP ₹ 40, SP ₹ 55. Profit or loss? How much?
  2. 2CP ₹ 120, SP ₹ 100. Profit or loss? How much?
  3. 3CP ₹ 75 and SP ₹ 75. What is the result?
Medium
  1. 4CP ₹ 600 and SP ₹ 720. Find the profit.
  2. 5CP ₹ 1,500 and SP ₹ 1,320. Find the loss.
  3. 6Flowers bought for ₹ 350 are sold for ₹ 500. Find the profit.
Challenging
  1. 7When is there a loss?
  2. 8The profit is ₹ 250 and the SP is ₹ 900. Find the CP.
Show answers (try them yourself first)
  1. 1Profit ₹ 15.
  2. 2Loss ₹ 20.
  3. 3No profit and no loss.
  4. 4₹ 120.
  5. 5₹ 180.
  6. 6₹ 150.
  7. 7When SP is less than CP.
  8. 8CP = 900 − 250 = ₹ 650.

Finding profit or loss

From daily life

A fruit seller buys 15 dozen bananas and sells them by the dozen. To find his result for the day he adds up what he spent and what he received, and compares.

Simple definition

First compare SP and CP, then subtract the smaller from the larger. For bulk goods, first find the total CP and the total SP.

Rule 1: Profit or loss from totals — CP ₹ 3,200 and SP ₹ 2,950 gives a loss of 3,200 − 2,950 = ₹ 250. A fruit seller buys 15 dozen bananas for ₹ 450 and sells at ₹ 40 per dozen. SP = 15 × 40 = 600, so profit = 600 − 450 = ₹ 150.

  • Easy : Easy: CP ₹ 500 and SP ₹ 560: profit ₹ 60.
  • Medium : Medium: 20 kg sugar bought for ₹ 800 and sold at ₹ 45 per kg: SP = 900 and profit = ₹ 100.
  • Exam-type : Exam: CP ₹ 3,200 and SP ₹ 2,950 give a loss of ₹ 250.

Rule 2: Spoiled goods — Spoiled or unsold goods bring no money, so count only the sold goods in SP. 200 kg onions cost ₹ 4,000. Only 180 kg are sold at ₹ 20, so SP = 180 × 20 = 3,600 and loss = 4,000 − 3,600 = ₹ 400.

Tomatoes: cost ₹8,208, sold for ₹7,950: loss ₹258.Cost price₹ 8,208Selling price318 × 25 = ₹ 7,950Loss 2588,208 − 7,950 = 25824 kg tomatoes spoiled, so they earned nothing

In the figure : In the figure tomatoes: loss ₹ 258.

  • Easy : Easy: 10 kg at ₹ 12 per kg is 10 × 12 = ₹ 120.
  • Medium : Medium: 50 pens cost ₹ 400. 5 are broken, 45 are sold at ₹ 10: SP = ₹ 450 and profit = ₹ 50.
  • Exam-type : Exam: 200 kg onions: loss = 4,000 − 3,600 = ₹ 400.
Live figure

Finding profit or loss

In the app you can move this figure with your finger.

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Remember

Compare, then subtract. Total = number × rate. Count only sold goods in SP.

Common mistake

Counting spoiled goods in SP. They earn nothing.

Shortcut

Memory clue: "आधी एकूण काढा, मग तुलना करा".

Spot the difference

StepAction
1Find total CP and total SP
2Compare
3Subtract smaller from larger

Practice questions

Easy
  1. 1CP ₹ 2,000 and SP ₹ 2,300. Find the profit.
  2. 2CP ₹ 900 and SP ₹ 840. Find the loss.
  3. 312 dozen eggs cost ₹ 960 and are sold at ₹ 90 per dozen. Find the profit.
Medium
  1. 440 kg rice cost ₹ 1,600 and is sold at ₹ 45 per kg. Find the profit.
  2. 5100 kg potatoes cost ₹ 1,500. 10 kg rot and 90 kg are sold at ₹ 15. Find the result.
  3. 630 notebooks cost ₹ 600 and each is sold at ₹ 18. Find the result.
Challenging
  1. 7CP ₹ 475 and SP ₹ 475. What is the result?
  2. 8Why do we first compare SP and CP?
Show answers (try them yourself first)
  1. 1₹ 300.
  2. 2₹ 60.
  3. 3SP = 12 × 90 = 1,080; profit ₹ 120.
  4. 4SP = 1,800; profit ₹ 200.
  5. 5SP = 1,350; loss ₹ 150.
  6. 6SP = 540; loss ₹ 60.
  7. 7Neither profit nor loss.
  8. 8To decide whether it is a profit or loss and which number to subtract from which.

Finding selling price or cost price

From daily life

A trader knows what he paid and how much profit he wants. He needs to fix the selling price. Another time he knows the SP and the profit and wants to know what he paid.

Simple definition

SP = CP + Profit or SP = CP − Loss. CP = SP − Profit or CP = SP + Loss.

Rule 1: Finding the selling price — CP ₹ 700 and profit ₹ 120 give SP = 700 + 120 = ₹ 820. CP ₹ 2,400 and loss ₹ 300 give SP = 2,400 − 300 = ₹ 2,100.

  • Easy : Easy: CP ₹ 500, profit ₹ 80: SP = ₹ 580.
  • Medium : Medium: CP ₹ 1,500, loss ₹ 200: SP = ₹ 1,300.
  • Exam-type : Exam: 8 pens bought at ₹ 10 each and sold at a profit of ₹ 3 each: SP of one = 13, SP of all = 8 × 13 = ₹ 104.

Rule 2: Finding the cost price and the six relations — SP ₹ 1,150 and profit ₹ 250 give CP = 1,150 − 250 = ₹ 900. SP ₹ 960 and loss ₹ 140 give CP = 960 + 140 = ₹ 1,100. Price of one item = total ÷ number: 15 shirts sold for ₹ 9,000 means ₹ 600 each.

Six handy relations of cost price, selling price, profit and loss.ProfitSP − CPLossCP − SPSelling priceCP + ProfitSelling priceCP − LossCost priceSP − ProfitCost priceSP + LossCP = cost price, SP = selling price

In the figure : In the figure six handy relations.

  • Easy : Easy: SP ₹ 300, profit ₹ 50: CP = ₹ 250.
  • Medium : Medium: SP ₹ 960, loss ₹ 140: CP = ₹ 1,100.
  • Exam-type : Exam: 15 shirts sold for ₹ 9,000 give ₹ 9,000 ÷ 15 = ₹ 600 each.
Remember

Profit: SP = CP + profit; CP = SP − profit. Loss: SP = CP − loss; CP = SP + loss.

Common mistake

Subtracting the loss when finding CP. For CP, add the loss to SP.

Shortcut

Memory clue: "नफ्यात SP मोठी, तोट्यात CP मोठी" (in profit, SP is bigger; in loss, CP is bigger).

Spot the difference

To findProfit caseLoss case
SPCP + profitCP − loss
CPSP − profitSP + loss

Practice questions

Easy
  1. 1CP ₹ 600 and profit ₹ 90. Find SP.
  2. 2CP ₹ 450 and loss ₹ 50. Find SP.
  3. 3SP ₹ 800 and profit ₹ 120. Find CP.
Medium
  1. 4SP ₹ 750 and loss ₹ 100. Find CP.
  2. 5CP ₹ 3,000 and profit ₹ 450. Find SP.
  3. 6SP ₹ 2,200 and loss ₹ 300. Find CP.
Challenging
  1. 78 bags are sold for ₹ 6,400. Find the price of one bag.
  2. 8Write the six relations of CP, SP, profit and loss.
Show answers (try them yourself first)
  1. 1₹ 690.
  2. 2₹ 400.
  3. 3₹ 680.
  4. 4₹ 850.
  5. 5₹ 3,450.
  6. 6₹ 2,500.
  7. 7₹ 800.
  8. 8Profit = SP − CP; Loss = CP − SP; SP = CP + Profit; SP = CP − Loss; CP = SP − Profit; CP = SP + Loss.

Total cost price

From daily life

A scooter bought second-hand needs repairs and paint before it is sold. These extra costs are part of what the seller really spent.

Simple definition

Along with the purchase price, other expenses such as transport, packing, repairs and wages are part of the cost: Total CP = Original CP + Other expenses.

Rule 1: Total cost price — Sunil bought a second-hand scooter for ₹ 40,000 and spent ₹ 5,000 on repairs and ₹ 3,000 on painting. Total CP = 40,000 + 5,000 + 3,000 = ₹ 48,000. Sold for ₹ 55,000, his profit is 55,000 − 48,000 = ₹ 7,000.

  • Easy : Easy: Goods ₹ 500 plus transport ₹ 50: total CP = ₹ 550.
  • Medium : Medium: Bought ₹ 2,500, repair ₹ 300, polish ₹ 200: total CP = ₹ 3,000.
  • Exam-type : Exam: Sunil sells the scooter for ₹ 45,000: loss = 48,000 − 45,000 = ₹ 3,000.

Rule 2: A crop example — A farmer spends ₹ 600 on seeds, ₹ 900 on fertiliser, ₹ 1,500 on labour and ₹ 500 on transport: total cost = 600 + 900 + 1,500 + 500 = ₹ 3,500. He sells 300 bundles at ₹ 20, so SP = ₹ 6,000 and profit = 6,000 − 3,500 = ₹ 2,500.

Akash: total cost 4,550, selling 11,250, profit 6,700.Total cost price = 4,550Seeds 850Manure 1,250Wages 1,650Transport 800Selling price = 450 × 25 = 11,250Profit 6,7004,550Include every expense in the cost price

In the figure : In the figure Akash: total cost, selling price and profit.

  • Easy : Easy: Add all expenses: 600 + 900 + 1,500 + 500 = ₹ 3,500.
  • Medium : Medium: SP = 300 × 20 = ₹ 6,000.
  • Exam-type : Exam: Profit = 6,000 − 3,500 = ₹ 2,500.
Remember

Total CP = purchase + other expenses. Then compare with SP.

Common mistake

Forgetting other expenses and finding profit from the purchase price alone.

Shortcut

Memory clue: "खरेदी + खर्च = एकूण CP".

Spot the difference

ItemPart of CP?
Purchase priceYes
Transport, repairsYes
Selling priceNo

Practice questions

Easy
  1. 1Goods ₹ 800 and transport ₹ 60. Find total CP.
  2. 2Bought ₹ 2,500, repairs ₹ 300 and polish ₹ 200. Find total CP.
  3. 3Total CP ₹ 3,000 and SP ₹ 3,400. Find the profit.
Medium
  1. 4Total CP ₹ 4,200 and SP ₹ 3,900. Find the loss.
  2. 520 kg bought at ₹ 40 per kg and ₹ 100 spent on transport. Sold at ₹ 50 per kg. Find the profit.
  3. 6A farmer spends ₹ 500, ₹ 700 and ₹ 300 and sells the crop for ₹ 2,200. Find the profit.
Challenging
  1. 7A car costs ₹ 3,00,000 and repairs cost ₹ 40,000. It is sold for ₹ 3,25,000. Find the result.
  2. 8Why are repair costs added to the cost price?
Show answers (try them yourself first)
  1. 1₹ 860.
  2. 2₹ 3,000.
  3. 3₹ 400.
  4. 4₹ 300.
  5. 5Total CP = 800 + 100 = 900; SP = 1,000; profit ₹ 100.
  6. 6Total cost 1,500; profit ₹ 700.
  7. 7Total CP ₹ 3,40,000; loss ₹ 15,000.
  8. 8They are money spent to get the goods ready for sale.

Word problems

From daily life

A women's self-help group buys flour and spices, makes papads, and sells them. At the end of the year the group must calculate the profit and share it fairly.

Simple definition

In a word problem, first find the total CP and the total SP, then compare them.

Rule 1: Steps and an example — A group spent ₹ 12,000 on papads and earned ₹ 17,000. Profit = 17,000 − 12,000 = ₹ 5,000. After giving ₹ 1,000 for social work, ₹ 4,000 is shared among 8 women: ₹ 500 each.

  • Easy : Easy: CP ₹ 90 and SP ₹ 120 give profit ₹ 30.
  • Medium : Medium: 6 chairs at ₹ 400 each cost ₹ 2,400 and sell at ₹ 450 each for ₹ 2,700; profit ₹ 300.
  • Exam-type : Exam: 20 kg mangoes bought at ₹ 60 per kg (₹ 1,200) plus ₹ 100 transport is ₹ 1,300. Sold at ₹ 75 per kg gives ₹ 1,500, so profit is ₹ 200.

Rule 2: Checking the answer — If you add the profit to the CP, you must get the SP. If you subtract the loss from the CP, you must get the SP. Example: CP ₹ 700, profit ₹ 80: 700 + 80 = 780 = SP ✓.

  • Easy : Easy: CP ₹ 90 + profit ₹ 30 = ₹ 120 = SP ✓.
  • Medium : Medium: CP ₹ 500 − loss ₹ 50 = ₹ 450 = SP ✓.
  • Exam-type : Exam: A loss of ₹ 150 on CP ₹ 1,200: SP = 1,200 − 150 = ₹ 1,050; check 1,200 − 1,050 = ₹ 150 ✓.
Remember

Total CP, total SP, compare. Check: CP + profit = SP; CP − loss = SP.

Common mistake

Stopping at the profit and forgetting to share or subtract what the question asks. Read the last line again.

Shortcut

Memory clue: "वाचा, एकूण काढा, तुलना करा, तपासा".

Spot the difference

StepAction
1Find total CP
2Find total SP
3Find profit or loss
4Check

Practice questions

Easy
  1. 1CP ₹ 250 and SP ₹ 300. Find the profit.
  2. 2CP ₹ 480 and SP ₹ 450. Find the loss.
  3. 36 chairs are bought at ₹ 400 each and sold at ₹ 450 each. Find the profit.
Medium
  1. 4CP ₹ 700 and profit ₹ 80. Find SP and check.
  2. 520 kg mangoes at ₹ 60 per kg plus ₹ 100 transport, sold at ₹ 75 per kg. Find the profit.
  3. 6A group spends ₹ 6,500 and earns ₹ 9,000. It gives ₹ 500 to charity and shares the rest among 4 women. How much does each get?
Challenging
  1. 7A loss of ₹ 150 is made on goods costing ₹ 1,200. Find the SP.
  2. 8How can you check that the SP ₹ 1,050 is right for CP ₹ 1,200 and loss ₹ 150?
Show answers (try them yourself first)
  1. 1₹ 50.
  2. 2₹ 30.
  3. 32,700 − 2,400 = ₹ 300.
  4. 4SP = ₹ 780; check 780 − 700 = 80 ✓.
  5. 5Total CP 1,300; SP 1,500; profit ₹ 200.
  6. 6Profit 2,500; after charity 2,000; each ₹ 500.
  7. 7₹ 1,050.
  8. 8CP − SP = 1,200 − 1,050 = 150, which equals the loss.