▶1. What is a partnership in business mathematics?
Answer: A partnership is when two or more people invest money to run a business and share the profits or losses.
Step-by-step Explanation:
1. Each partner invests some money (capital).
2. The business earns profit or loss.
3. The profit or loss is shared among partners, usually in the ratio of their investments and the time for which the money is invested.
4. Example: If A and B start a business together, they are partners.
▶2. If A and B invest ₹10,000 and ₹20,000 respectively in a business, what is their profit sharing ratio?
Answer: 1:2
Step-by-step Explanation:
1. Profit sharing ratio = Investment of A : Investment of B.
2. So, 10,000 : 20,000 = 1:2.
3. B will get twice the profit of A.
▶3. If A invests ₹5,000 for 12 months and B invests ₹10,000 for 6 months, what is their profit sharing ratio?
Answer: 1:1
Step-by-step Explanation:
1. Multiply each investment by the time invested.
2. A: 5,000 × 12 = 60,000.
3. B: 10,000 × 6 = 60,000.
4. Ratio = 60,000:60,000 = 1:1.
5. Both get equal profit.
▶4. A and B invest ₹8,000 and ₹12,000 respectively. After 6 months, A withdraws his money. If the business runs for 1 year, what is their profit sharing ratio?
Answer: 1:2
Step-by-step Explanation:
1. A: 8,000 × 6 = 48,000.
2. B: 12,000 × 12 = 1,44,000.
3. Ratio = 48,000:1,44,000 = 1:3.
4. So, B gets three times A's profit.
▶5. If A and B invest ₹15,000 and ₹10,000 for 8 months and 12 months respectively, what is their profit sharing ratio?
Answer: 1:1
Step-by-step Explanation:
1. A: 15,000 × 8 = 1,20,000.
2. B: 10,000 × 12 = 1,20,000.
3. Ratio = 1,20,000:1,20,000 = 1:1.
4. Both get equal profit.
▶6. A, B, and C invest ₹6,000, ₹8,000, and ₹10,000 for 1 year. What is their profit sharing ratio?
Answer: 3:4:5
Step-by-step Explanation:
1. Ratio = 6,000:8,000:10,000 = 3:4:5.
2. C gets the largest share, A the smallest.
▶7. If A and B invest ₹12,000 and ₹18,000 for 9 months and 6 months respectively, what is their profit sharing ratio?
Answer: 2:1
Step-by-step Explanation:
1. A: 12,000 × 9 = 1,08,000.
2. B: 18,000 × 6 = 1,08,000.
3. Ratio = 1,08,000:1,08,000 = 1:1.
4. Both get equal profit.
▶8. A and B start a business. A invests ₹10,000 for 10 months, B invests ₹15,000 for 8 months. If the profit is ₹4,600, what is A's share?
Answer: ₹2,300
Step-by-step Explanation:
1. A: 10,000 × 10 = 1,00,000.
2. B: 15,000 × 8 = 1,20,000.
3. Ratio = 1,00,000:1,20,000 = 5:6.
4. A's share = (5/11) × 4,600 = ₹2,090.91 (rounded to ₹2,091).
▶9. A, B, and C invest ₹8,000, ₹12,000, and ₹16,000 for 6, 8, and 10 months respectively. If the profit is ₹9,600, what is B's share?
Answer: ₹2,400
Step-by-step Explanation:
1. A: 8,000 × 6 = 48,000.
2. B: 12,000 × 8 = 96,000.
3. C: 16,000 × 10 = 1,60,000.
4. Total = 48,000 + 96,000 + 1,60,000 = 3,04,000.
5. B's share = (96,000/3,04,000) × 9,600 = ₹3,028.95 (rounded to ₹3,029).
▶10. A and B invest ₹5,000 and ₹7,000. After 6 months, A adds ₹3,000 more. If the business runs for 1 year, what is their profit sharing ratio?
Answer: 11:14
Step-by-step Explanation:
1. A: (5,000 × 6) + (8,000 × 6) = 30,000 + 48,000 = 78,000.
2. B: 7,000 × 12 = 84,000.
3. Ratio = 78,000:84,000 = 13:14.
▶11. A, B, and C invest ₹10,000, ₹20,000, and ₹30,000 for 4, 6, and 8 months. If the profit is ₹12,000, what is C's share?
Answer: ₹6,000
Step-by-step Explanation:
1. A: 10,000 × 4 = 40,000.
2. B: 20,000 × 6 = 1,20,000.
3. C: 30,000 × 8 = 2,40,000.
4. Total = 40,000 + 1,20,000 + 2,40,000 = 4,00,000.
5. C's share = (2,40,000/4,00,000) × 12,000 = ₹7,200.
▶12. A and B invest ₹6,000 and ₹9,000. After 4 months, A withdraws ₹2,000. If the business runs for 1 year, what is their profit sharing ratio?
Answer: 7:9
Step-by-step Explanation:
1. A: (6,000 × 4) + (4,000 × 8) = 24,000 + 32,000 = 56,000.
2. B: 9,000 × 12 = 1,08,000.
3. Ratio = 56,000:1,08,000 = 7:13.
▶13. A and B invest ₹10,000 and ₹15,000 for 8 and 12 months. If the profit is ₹5,400, what is B's share?
Answer: ₹3,600
Step-by-step Explanation:
1. A: 10,000 × 8 = 80,000.
2. B: 15,000 × 12 = 1,80,000.
3. Total = 80,000 + 1,80,000 = 2,60,000.
4. B's share = (1,80,000/2,60,000) × 5,400 = ₹3,738.46 (rounded to ₹3,738).
▶14. A, B, and C invest ₹12,000, ₹18,000, and ₹24,000 for 6, 8, and 10 months. If the profit is ₹9,000, what is A's share?
Answer: ₹1,200
Step-by-step Explanation:
1. A: 12,000 × 6 = 72,000.
2. B: 18,000 × 8 = 1,44,000.
3. C: 24,000 × 10 = 2,40,000.
4. Total = 72,000 + 1,44,000 + 2,40,000 = 4,56,000.
5. A's share = (72,000/4,56,000) × 9,000 = ₹1,421.05 (rounded to ₹1,421).
▶15. A and B invest ₹20,000 and ₹30,000. After 6 months, A adds ₹10,000 more. If the business runs for 1 year, what is their profit sharing ratio?
Answer: 7:9
Step-by-step Explanation:
1. A: (20,000 × 6) + (30,000 × 6) = 1,20,000 + 1,80,000 = 3,00,000.
2. B: 30,000 × 12 = 3,60,000.
3. Ratio = 3,00,000:3,60,000 = 5:6.
▶16. A, B, and C invest ₹10,000, ₹20,000, and ₹30,000. After 4 months, A withdraws ₹5,000, B adds ₹5,000, and C withdraws ₹10,000. If the business runs for 1 year, what is their profit sharing ratio?
Answer: 7:13:15
Step-by-step Explanation:
1. A: (10,000 × 4) + (5,000 × 8) = 40,000 + 40,000 = 80,000.
2. B: (20,000 × 4) + (25,000 × 8) = 80,000 + 2,00,000 = 2,80,000.
3. C: (30,000 × 4) + (20,000 × 8) = 1,20,000 + 1,60,000 = 2,80,000.
4. Ratio = 80,000:2,80,000:2,80,000 = 2:7:7.
▶17. A and B invest ₹15,000 and ₹25,000. After 8 months, B withdraws ₹5,000. If the business runs for 1 year, what is their profit sharing ratio?
Answer: 19:29
Step-by-step Explanation:
1. A: 15,000 × 12 = 1,80,000.
2. B: (25,000 × 8) + (20,000 × 4) = 2,00,000 + 80,000 = 2,80,000.
3. Ratio = 1,80,000:2,80,000 = 9:14.
▶18. A, B, and C invest ₹8,000, ₹12,000, and ₹16,000 for 6, 8, and 10 months. If the profit is ₹12,000, what is B's share?
Answer: ₹3,200
Step-by-step Explanation:
1. A: 8,000 × 6 = 48,000.
2. B: 12,000 × 8 = 96,000.
3. C: 16,000 × 10 = 1,60,000.
4. Total = 48,000 + 96,000 + 1,60,000 = 3,04,000.
5. B's share = (96,000/3,04,000) × 12,000 = ₹3,789.47 (rounded to ₹3,789).
▶19. A and B invest ₹10,000 and ₹20,000 for 6 and 12 months. If the profit is ₹6,000, what is A's share?
Answer: ₹1,000
Step-by-step Explanation:
1. A: 10,000 × 6 = 60,000.
2. B: 20,000 × 12 = 2,40,000.
3. Total = 60,000 + 2,40,000 = 3,00,000.
4. A's share = (60,000/3,00,000) × 6,000 = ₹1,200.
▶20. A, B, and C invest ₹5,000, ₹10,000, and ₹15,000 for 12, 8, and 6 months. If the profit is ₹9,000, what is C's share?
Answer: ₹1,500
Step-by-step Explanation:
1. A: 5,000 × 12 = 60,000.
2. B: 10,000 × 8 = 80,000.
3. C: 15,000 × 6 = 90,000.
4. Total = 60,000 + 80,000 + 90,000 = 2,30,000.
5. C's share = (90,000/2,30,000) × 9,000 = ₹3,521.74 (rounded to ₹3,522).
▶ A car is sold for ₹2400 at a profit of 20%. What is the CP?
Options: (a) ₹2100 (b) ₹2000 (c) ₹1800 (d) ₹2200
Solution:
1. Let CP = x.
2. Profit = 20% of x = 0.2x.
3. SP = CP + Profit = x + 0.2x = 1.2x.
4. Given SP = ₹2400:
1.2x = 2400 ⇒ x = 2400/1.2 = 2000.
Answer: (b) ₹2000
▶ A car is sold for ₹2400 at a profit of 20% over SP. What is the CP?
Options: (a) ₹2000 (b) ₹1920 (c) ₹1980 (d) ₹1800
Solution:
1. Profit = 20% of SP = 0.2 × 2400 = 480.
2. CP = SP - Profit = 2400 - 480 = 1920.
Answer: (b) ₹1920
▶ A car is sold for ₹2400 at a profit of 20% over SP. What is the actual profit percentage?
Options: (a) 16.66% (b) 25% (c) 21.21% (d) 14.28%
Solution:
1. CP = ₹1920, SP = ₹2400.
2. Profit = 2400 - 1920 = 480.
3. Profit % over CP = (480/1920) × 100 = 25%.
Answer: (b) 25%
▶ Apples are purchased at 10 apples/₹. How many apples should be sold for ₹1 to obtain a profit of 25%?
Options: (a) 6 (b) 8 (c) 12 (d) 4
Solution:
1. CP of 10 apples = ₹1 ⇒ CP per apple = ₹0.10.
2. To get 25% profit, SP per apple = 0.10 × 1.25 = ₹0.125.
3. Number of apples sold for ₹1 = 1/0.125 = 8.
Answer: (b) 8
▶ Sharat sells to Chandra at 20% profit, Chandra sells to Mayank at 30% loss, Mayank sells at 20% profit. If Chandra's CP is ₹150, find Mayank's SP.
Options: (a) ₹105 (b) ₹87.5 (c) ₹125 (d) ₹126
Solution:
1. Sharat to Chandra: CP = 150/1.2 = 125.
2. Chandra to Mayank: SP = 150 × 0.7 = 105.
3. Mayank's Sale: SP = 105 × 1.2 = 126.
Answer: (d) ₹126
▶ Petrol is purchased at ₹5/L and sold at 5L/₹. What is the profit/loss %?
Options: (a) Loss of 96% (b) No profit, no loss (c) Profit of 2400% (d) None of these
Solution:
1. CP for 5L = 5 × 5 = ₹25.
2. SP for 5L = ₹1.
3. Loss = 25 - 1 = ₹24.
4. Loss % = (24/25) × 100 = 96%.
Answer: (a) Loss of 96%
▶ After an 11.11% discount on the marked price, profit is 14.28%. Find the % mark-up over CP.
Options: (a) 14.28% (b) 28.56% (c) 25% (d) 50%
Solution:
1. Let CP = ₹100.
2. Profit = 14.28% ⇒ SP = ₹114.28.
3. Discount = 11.11% ⇒ MP = 114.28/0.8889 ≈ 128.56.
4. Mark-up % = (128.56 - 100)/100 × 100 = 28.56%.
Answer: (b) 28.56%
▶ A shopkeeper wants 20% profit and offers a 25% discount. Find the minimum % mark-up over CP.
Options: (a) 60% (b) 42.5% (c) 62.5% (d) 35%
Solution:
1. Let CP = ₹100.
2. Desired SP = ₹120 (20% profit).
3. Discount = 25% ⇒ MP = 120/0.75 = 160.
4. Mark-up % = (160 - 100)/100 × 100 = 60%.
Answer: (a) 60%
▶ An article sold at 10% discount gives a profit of ₹70. What is the CP?
Options: (a) ₹700 (b) ₹350 (c) ₹125 (d) Cannot be determined
Solution:
- Insufficient data to determine CP uniquely.
Answer: (d) Cannot be determined
▶ 100 kg of gold is purchased for ₹1100. It is sold such that the total loss equals the amount obtained by selling 20 kg of gold. Find the selling price per kg.
Options: (a) ₹9.16 (b) ₹18.32 (c) ₹11.11 (d) ₹25
Solution:
1. Let SP per kg = x.
2. Total SP = 100x.
3. Loss = 1100 - 100x.
4. Given loss = SP of 20 kg = 20x.
5. 1100 - 100x = 20x ⇒ 1100 = 120x ⇒ x = 1100/120 = 9.16.
Answer: (a) ₹9.16
▶ A milkman buys two cows for ₹750. He sells the first cow at 22% profit and the second cow at 8% loss, with no overall profit or loss. Find the SP of the second cow.
Options: (a) ₹312 (b) ₹506 (c) ₹484 (d) ₹532
Solution:
1. Let CP of first cow = x, CP of second cow = 750 - x.
2. SP of first cow = 1.22x.
3. SP of second cow = 0.92(750 - x).
4. 1.22x + 0.92(750 - x) = 750 ⇒ 0.3x = 60 ⇒ x = 200.
5. SP of second cow = 0.92 × 550 = 506.
Answer: (b) ₹506
▶ Two cars are sold for ₹24,000 each. One is sold at 20% profit and the other at 20% loss. Find the net profit/loss percentage and amount.
Options: (a) 4% profit, ₹2000 profit (b) 4% loss, ₹2000 loss (c) 1% profit, ₹500 profit (d) 1% loss, ₹500 loss
Solution:
1. First Car (Profit): CP = 24000/1.2 = 20000.
2. Second Car (Loss): CP = 24000/0.8 = 30000.
3. Total CP = 20000 + 30000 = 50000.
4. Total SP = 24000 + 24000 = 48000.
5. Loss = 50000 - 48000 = 2000.
6. Loss % = (2000/50000) × 100 = 4%.
Answer: (b) 4% loss, ₹2000 loss
▶ A supplier sells 20 pencils at the marked price of 16 pens to a retailer, who sells them at the marked price. What is the retailer's profit percentage?
Options: (a) Loss 25% (b) Profit 25% (c) Loss 20% (d) Profit 20%
Solution:
1. Let MP of 1 pen = ₹1 ⇒ MP of 16 pens = ₹16.
2. Retailer buys 20 pencils for ₹16 ⇒ CP per pencil = ₹0.80.
3. Retailer sells at MP ⇒ SP per pencil = ₹1.
4. Profit % = (1 - 0.8)/0.8 × 100 = 25%.
Answer: (b) Profit 25%
▶ Sum of CPs of two cars is ₹1,00,000. First car is sold at 20% profit and second at 20% loss, with equal SPs. Find CP of first car.
Options: (a) ₹40,000 (b) ₹60,000 (c) ₹52,400 (d) ₹47,600
Solution:
1. Let CP of first car = x, CP of second car = 100000 - x.
2. SP of first car = 1.2x.
3. SP of second car = 0.8(100000 - x).
4. 1.2x = 0.8(100000 - x) ⇒ 1.2x = 80000 - 0.8x ⇒ 2x = 80000 ⇒ x = 40000.
Answer: (a) ₹40,000
▶ Sum of CPs of two cows is ₹13,000. Both are sold at 20% and 40% profit, respectively, with equal SPs. Find the difference in CPs.
Options: (a) ₹1000 (b) ₹2000 (c) ₹1500 (d) ₹2500
Solution:
1. Let CPs be x and 13000 - x.
2. 1.2x = 1.4(13000 - x) ⇒ 1.2x = 18200 - 1.4x ⇒ 2.6x = 18200 ⇒ x = 7000.
3. Difference = 13000 - 7000 - 7000 = 1000.
Answer: (a) ₹1000
▶ "Buy three, get one free." What is the discount percentage?
Options: (a) 33.33% (b) 25% (c) 20% (d) 28.56%
Solution:
1. Effective price for 4 items = Price of 3.
2. Discount % = (1/4) × 100 = 25%.
Answer: (b) 25%
▶ CP of 40 articles = SP of 30 articles. Find profit/loss percentage.
Options: (a) 25% profit (b) 33.33% profit (c) 25% loss (d) 33.33% loss
Solution:
1. Let CP per article = ₹1 ⇒ CP of 40 = ₹40 = SP of 30.
2. SP per article = 40/30 = ₹1.33.
3. Profit % = (1.33 - 1)/1 × 100 = 33.33%.
Answer: (b) 33.33% profit
▶ Due to a 20% price hike, 4 kg less tea is available for ₹120. Find original price.
Options: (a) ₹4/kg (b) ₹5/kg (c) ₹6/kg (d) ₹4.5/kg
Solution:
1. Let original price = x/kg.
2. New price = 1.2x/kg.
3. (120/x) - (120/1.2x) = 4 ⇒ (120(1.2 - 1))/(1.2x) = 4 ⇒ 24/(1.2x) = 4 ⇒ x = 5.
Answer: (b) ₹5/kg
▶ A shopkeeper sells at CP but uses 750 g instead of 1000 g. Find profit percentage.
Options: (a) 25% (b) 20% (c) 16.66% (d) 33.33%
Solution:
1. Charges for 1000 g but gives 750 g.
2. Profit % = (1000 - 750)/750 × 100 = 33.33%.
Answer: (d) 33.33%
▶ A shopkeeper sells goods at cost price but manipulates weights to gain 30% profit. How many grams is he actually giving for 1000 g?
Options: (a) 700 (b) 769 (c) 800 (d) 820
Solution:
1. Let CP for 1000 g = ₹1000.
2. SP for 1000 g = ₹1000 (sold at CP).
3. But he gains 30%, so actual CP for the quantity sold = 1000/1.3 ≈ 769.23.
4. Thus, actual weight given = 769 g.
Answer: (b) 769
▶ Which discount option is better for a customer? (i) Successive discounts of 20%, 30%, then 10% tax. (ii) Successive discounts of 30%, 20%, then 10% tax. (iii) Pay 10% tax first, then discounts of 20% and 30%.
Options: (a) (i) or (ii) (b) (iii) (c) Either of these three (d) (i) and (iii) or (ii) and (iii)
Solution:
1. For (i) and (ii): Final price = P × 0.8 × 0.7 × 1.10 = P × 0.616.
2. For (iii): Final price = P × 1.10 × 0.8 × 0.7 = P × 0.616.
3. All options are equivalent.
Answer: (c) Either of these three
▶ A wholesaler sells chips at ₹10,000 each with 5% defective, replaced freely. He still makes 20% profit. Find selling price.
Options: (a) ₹12,300 (b) ₹12,600 (c) ₹13,200 (d) None
Solution:
1. For every 100 chips: CP = 10,000 × 100 = 1,000,000.
2. 5 defective replaced ⇒ Total sold = 100, but CP is for 105 chips.
3. Effective CP per chip = 1,000,000/100 = 10,000.
4. Desired profit = 20% ⇒ SP = 10,000 × 1.20 = 12,000.
Answer: (d) None (Correct answer is ₹12,000)
▶ A seller calculates SP at 6% profit but interchanges digits, reducing profit by ₹9 and profit% to 2.4%. Find CP.
Options: (a) ₹240 (b) ₹250 (c) ₹400 (d) ₹480
Solution:
1. Let CP = x.
2. Intended SP = 1.06x.
3. Incorrect SP (digits swapped) = 1.06x - 9.
4. New profit % = 2.4% ⇒ SP = 1.024x.
5. 1.06x - 9 = 1.024x ⇒ 0.036x = 9 ⇒ x = 250.
Answer: (b) ₹250
▶ A shopkeeper calculates profit on SP as 25%. Find actual profit %.
Options: (a) 20% (b) 33.33% (c) 40% (d) 25%
Solution:
1. Let SP = ₹100.
2. Profit on SP = 25% ⇒ Profit = ₹25 ⇒ CP = ₹75.
3. Actual profit % on CP = (25/75) × 100 = 33.33%.
Answer: (b) 33.33%
▶ Two shopkeepers sell the same article: First offers 25% discount. Second offers 25% more quantity for same price. Which deal is better?
Options: (a) First (b) Second (c) Both equal (d) Cannot determine
Solution:
1. First Shopkeeper: Effective price = 75% of original.
2. Second Shopkeeper: For same price, get 1.25 units ⇒ Effective price per unit = 1/1.25 = 80% of original.
3. 75% > 80% ⇒ First deal is better.
Answer: (a) First
▶ CP of first cow = SP of second cow, and SP of first cow = CP of second cow. What is the net result?
Options: (a) Loss (b) Profit (c) No profit/loss (d) Cannot determine
Solution:
1. Let CP of first cow = SP of second cow = x.
2. SP of first cow = CP of second cow = y.
3. Net result: Profit on first cow = y - x. Loss on second cow = y - x.
4. Net profit/loss = 0.
Answer: (c) No profit, no loss
▶ An article sold for ₹180 gives 20% profit. What should be SP for double profit %?
Options: (a) ₹200 (b) ₹210 (c) ₹192 (d) ₹240
Solution:
1. CP = 180/1.20 = 150.
2. Double profit % = 40% ⇒ SP = 150 × 1.40 = 210.
Answer: (b) ₹210
▶ Vinit sells to Amit at 20% profit, Amit to Vicky at 12% profit, Vicky to Nishu at 21% loss. Find sum of CPs of Amit and Nishu.
Options: (a) ₹250 (b) ₹475 (c) ₹540 (d) Cannot determine
Solution:
1. Let Vinit's CP = x.
2. Amit's CP = 1.20x.
3. Vicky's CP = 1.20x × 1.12 = 1.344x.
4. Nishu's CP = 1.344x × 0.79 = 1.06176x.
5. Sum of Amit and Nishu's CPs = 1.20x + 1.06176x = 2.26176x. Cannot determine without x.
Answer: (d) Cannot determine
▶ Anoop sells to Mayank at 20% profit, Mayank to Siddharth at 25% profit, Siddharth to Shishir at 10% loss. What loss % should Shishir sell at to match Anoop's CP?
Options: (a) 36.68% (b) 25.92% (c) 48.66 (d) Cannot determine
Solution:
1. Anoop's CP = 100.
2. Mayank's CP = 120.
3. Siddharth's CP = 120 × 1.25 = 150.
4. Shishir's CP = 150 × 0.90 = 135.
5. To match Anoop's CP (100), Shishir's loss = (135 - 100)/135 × 100 = 25.92%.
Answer: (b) 25.92%