Question 1

Finding time ratios from profit and capital ratios: A, B, C invested capitals in the ratio 5 : 6 : 8, but received profits in the ratio 5 : 3 : 1. Determine the ratio of time for which their capitals were invested.

Accepted Answer

Introduction / Context: Profit in partnerships is proportional to capital × time. If we know both the capital ratio and the final profit ratio, we can back out the time ratio by dividing profit parts by capital parts for each partner. This technique is widely used to resolve differing investment durations.Given Data / Assumptions:Capital ratio (A : B : C) = 5 : 6 : 8.Profit ratio (A : B : C) = 5 : 3 : 1.Profit ∝ capital * time ⇒ time ∝ profit / capital.Concept / Approach: Compute time ratios as (profit_i / capital_i) for each partner and then scale to whole numbers by a common factor to remove fractions.Step-by-Step Solution:t_A ∝ 5/5 = 1.t_B ∝ 3/6 = 1/2.t_C ∝ 1/8 = 1/8.Multiply by 8 to clear denominators ⇒ 8 : 4 : 1.Verification / Alternative check: Check: capital × time ⇒ A 5*8=40, B 6*4=24, C 8*1=8 ⇒ profit parts 40:24:8 = 5:3:1 after dividing by 8, consistent with the given profit ratio.Why Other Options Are Wrong: Other options fail to produce the stated profit ratio when multiplied by capital parts; only 8 : 4 : 1 satisfies profit ∝ capital × time exactly.Common Pitfalls: Inverting the relationship (capital/time) or trying to subtract ratios instead of dividing; always use profit / capital to get time parts.Final Answer: 8 : 4 : 1

Question 2

Linking successive percentage relations in investments: Sonu invested 10% more than Mona, and Mona invested 10% less than Raghu. If their combined investment is ₹ 5,780, find Raghu’s investment.

Accepted Answer

Introduction / Context: This is a chained-percentage linkage problem. Express each person’s investment in terms of Raghu’s base amount R. Then sum the three expressions, set equal to the given total, and solve for R. Percentage increases/decreases convert directly to multipliers (1.10 for +10%, 0.90 for −10%).Given Data / Assumptions:Mona = 10% less than Raghu ⇒ Mona = 0.9R.Sonu = 10% more than Mona ⇒ Sonu = 1.1 * Mona = 1.1 * 0.9R = 0.99R.Total = Sonu + Mona + Raghu = ₹ 5,780.Concept / Approach: Replace all amounts with R expressions and solve a single linear equation in R. This avoids guesswork and ensures consistency with both percentage statements.Step-by-Step Solution:Total = 0.99R + 0.90R + 1.00R = 2.89R.2.89R = 5,780 ⇒ R = 5,780 / 2.89 = ₹ 2,000.Verification / Alternative check: Mona = 0.9*2,000 = ₹ 1,800; Sonu = 0.99*2,000 = ₹ 1,980. Sum = 1,980 + 1,800 + 2,000 = ₹ 5,780, exactly the given total.Why Other Options Are Wrong: ₹ 2,100, ₹ 2,010, ₹ 2,210, ₹ 1,990 fail to satisfy both chained percentage conditions when recomputed and summed to ₹ 5,780.Common Pitfalls: Applying +10% to Raghu directly for Sonu, or combining percentages additively (10% − 10% = 0%) instead of multiplicatively (1.1 * 0.9 = 0.99).Final Answer: ₹ 2000

Question 3

Sharing profit when one partner gets a fixed fraction: A, B, and C share profit such that A receives 3/5 of the total, while B and C split the remaining equally. If C receives ₹ 400 less than A, find the total profit.

Accepted Answer

Introduction / Context: Here, the shares are specified in fractions of the whole: A has 3/5, and the remaining 2/5 is divided equally between B and C. A linear relation between A’s and C’s amounts is given (C is ₹ 400 less than A). Translate these to equations in the total profit T and solve for T directly.Given Data / Assumptions:A = (3/5)T.B = C = (1/5)T.A − C = ₹ 400.Concept / Approach: Substitute A and C in terms of T into the difference equation A − C = 400. This yields a simple equation in T; once T is known, all individual shares follow automatically.Step-by-Step Solution:A − C = (3/5)T − (1/5)T = (2/5)T.(2/5)T = 400 ⇒ T = 400 * (5/2) = ₹ 1,000.Thus A = ₹ 600, B = ₹ 200, C = ₹ 200 (indeed, A − C = 400).Verification / Alternative check: Fractions sum: (3/5) + (1/5) + (1/5) = 1. Their values at T = 1,000 are ₹ 600, ₹ 200, ₹ 200, totaling ₹ 1,000.Why Other Options Are Wrong: ₹ 1,200, ₹ 1,600, and ₹ 800 would yield A − C values other than ₹ 400; ₹ 2,000 doubles all shares and breaks the given difference condition.Common Pitfalls: Assuming equal shares among all three or misreading “remaining profit equally” as “A, B, C equally.”Final Answer: ₹ 1000

Question 4

Finding the joining time from a profit ratio: A begins with ₹ 2,250. B later joins with ₹ 2,700. At year end, profits are divided in the ratio 2 : 1 (A : B). After how many months did B join?

Accepted Answer

Introduction / Context: When profits are divided in a known ratio, and the capitals are known, we can find the missing time for a late entrant by equating the capital × time weights to the profit ratio. This is a straightforward application of proportional reasoning in partnerships.Given Data / Assumptions:A’s capital = ₹ 2,250 for 12 months.B’s capital = ₹ 2,700 for t months (unknown).Profit ratio A : B = 2 : 1.Concept / Approach: Profit ratio equals the ratio of capital × time. Set up 2,250*12 : 2,700*t = 2 : 1 and solve for t. Ensure proper simplification to avoid arithmetic slips.Step-by-Step Solution:A weight = 2,250 * 12 = 27,000.27,000 : 2,700t = 2 : 1 ⇒ divide by 2,700 ⇒ 10 : t = 2 : 1.10/t = 2 ⇒ t = 5 months.Verification / Alternative check: B weight = 2,700*5 = 13,500. A : B weights = 27,000 : 13,500 = 2 : 1, matching the profit ratio.Why Other Options Are Wrong: 3, 4, 6, 7 months do not yield the stated 2 : 1 profit split when converted to weights with given capitals.Common Pitfalls: Using 12 months for both partners or failing to divide by the common factor correctly when simplifying the proportion.Final Answer: 5 months

Question 5

Deriving time ratio from given capital and profit ratios: A, B, and C invested in the ratio 4 : 6 : 9 and received profit in the ratio 2 : 3 : 5. Find the ratio of time for which their capitals were invested.

Accepted Answer

Introduction / Context: Profit is proportional to capital × time. With known capital and profit ratios, we can recover time parts by dividing profit parts by capital parts for each partner. This inverse approach is essential for handling varying durations of investment in partnerships.Given Data / Assumptions:Capital ratio (A : B : C) = 4 : 6 : 9.Profit ratio (A : B : C) = 2 : 3 : 5.Time ∝ profit / capital.Concept / Approach: Compute time parts: t_A ∝ 2/4, t_B ∝ 3/6, t_C ∝ 5/9. Convert to a whole-number ratio by clearing denominators through a common multiple (here, 18).Step-by-Step Solution:t_A ∝ 2/4 = 1/2.t_B ∝ 3/6 = 1/2.t_C ∝ 5/9.Scale by 18: A 9, B 9, C 10 ⇒ ratio = 9 : 9 : 10.Verification / Alternative check: Multiply capital by time: A 4*9=36, B 6*9=54, C 9*10=90 ⇒ 36:54:90 reduces to 2:3:5, confirming the profit ratio.Why Other Options Are Wrong: Other choices do not reproduce the given profit ratio when combined with the capital ratio via capital × time.Common Pitfalls: Using capital/time instead of profit/capital, or forgetting to scale to clear denominators properly.Final Answer: 9 : 9 : 10

Question 6

Updated profit-sharing ratio after increasing investments: Aarti, Vinita, and Kamla invest in the ratio 5 : 7 : 6 initially. Next year they increase investments by 26%, 20%, and 15% respectively. Find the ratio in which the second-year profit should…

Accepted Answer

Introduction / Context: Profit in a year is proportional to the invested capital for that year. When investments change by given percentages, multiply each base part by (1 + percentage change) to get the effective parts for that year, then reduce to a clean ratio for distribution.Given Data / Assumptions:Initial ratio: 5 : 7 : 6.Increases: Aarti +26%, Vinita +20%, Kamla +15%.Second-year profit ∝ updated capitals.Concept / Approach: Multiply each initial part by the growth factor: 1.26, 1.20, 1.15 respectively, then convert to integers by scaling (e.g., multiply by 10) and simplify if possible.Step-by-Step Solution:Aarti: 5 * 1.26 = 6.30.Vinita: 7 * 1.20 = 8.40.Kamla: 6 * 1.15 = 6.90.Scale by 10 ⇒ 63 : 84 : 69 ⇒ divide by 3 ⇒ 21 : 28 : 23.Verification / Alternative check: Any common multiplier applied to 21 : 28 : 23 corresponds to the same proportional distribution; thus this ratio uniquely represents the second-year split.Why Other Options Are Wrong: Other options do not preserve the precise 1.26, 1.20, and 1.15 factors applied to 5 : 7 : 6.Common Pitfalls: Adding percentage points directly to the ratio numbers instead of multiplying by growth factors; failing to simplify properly.Final Answer: 21 : 28 : 23

Question 7

Managing partner’s commission with remaining profit shared by capital: Anil (active) invests ₹ 12,000, Vimal (sleeping) invests ₹ 20,000. Anil gets 10% of total profit for managing; the remaining profit is shared in the ratio of capitals. If total p…

Accepted Answer

Introduction / Context: In partnerships with a managing partner, a fixed percentage of the total profit may be paid as commission before the remainder is split by capital ratios. This two-stage allocation must be handled sequentially to avoid errors in the final amounts received by each partner.Given Data / Assumptions:Anil capital = ₹ 12,000; Vimal capital = ₹ 20,000.Total profit = ₹ 9,000.Managing commission for Anil = 10% of total profit.Remaining profit divided in ratio 12,000 : 20,000 = 3 : 5.Concept / Approach: First deduct the 10% commission from total profit; then share the balance by the capital ratio. Add the commission back to Anil’s share from the remainder to get his total receipt.Step-by-Step Solution:Commission = 10% * 9,000 = ₹ 900 (to Anil).Balance = 9,000 − 900 = ₹ 8,100.Anil’s share of balance = 8,100 * (3/8) = ₹ 3,037.50.Total to Anil = 900 + 3,037.50 = ₹ 3,937.50.Verification / Alternative check: Vimal’s share of balance = 8,100 * (5/8) = ₹ 5,062.50. Sum with Anil’s 3,937.50 equals ₹ 9,000 total profit, confirming correctness.Why Other Options Are Wrong: ₹ 4,500, ₹ 4,800, and ₹ 4,600 assume different commission handling or equal division; ₹ 4,200 miscomputes the capital-based split.Common Pitfalls: Sharing first then taking commission, or taking 10% of the remaining profit rather than 10% of the total, as specified.Final Answer: ₹ 3937.5

Question 8

Inferring a partner’s time from profit share and capital fractions: Aayush provides 1/4 of the capital for 15 months. Babloo receives 2/3 of the profit. Assuming only two partners, for how many months was Babloo’s money used?

Accepted Answer

Introduction / Context: Profit shares in partnerships are proportional to capital × time. With only two partners, if one partner’s capital fraction and time are known, and the profit split is given, we can solve for the other partner’s time from a single proportion equation.Given Data / Assumptions:Aayush capital fraction = 1/4, time = 15 months.Babloo capital fraction = 3/4 (rest of the capital), time = t months.Babloo’s profit share = 2/3; hence Aayush’s share = 1/3.Concept / Approach: Set the ratio of profit shares equal to the ratio of capital × time contributions: (Babloo : Aayush) = ((3/4)*t) : ((1/4)*15) = 2 : 1. Solve for t directly.Step-by-Step Solution:((3/4)*t) / ((1/4)*15) = 2/1.(3t)/15 = 2 ⇒ 3t = 30 ⇒ t = 10 months.Verification / Alternative check: Weights: Aayush = (1/4)*15 = 3.75; Babloo = (3/4)*10 = 7.5 ⇒ ratio 7.5 : 3.75 = 2 : 1, consistent with the given profit split.Why Other Options Are Wrong: 9, 11, 7, 12 months do not produce a 2 : 1 profit ratio when combined with the stated capital fractions.Common Pitfalls: Using 1/4 and 3/4 as months rather than capital fractions or mixing up which partner gets 2/3 of the profit.Final Answer: 10 months

Question 9

Dividing a premium for sacrificing future profit share: A and B initially share profit in the ratio of their capitals ₹ 20,000 : ₹ 35,000 (i.e., 4 : 7). C joins so that A, B, C will share profits equally. C pays a premium ₹ 2,20,000 to compensate A …

Accepted Answer

Introduction / Context: When a new partner joins and the sharing ratio changes, existing partners sacrifice part of their future profit. Any premium paid for this sacrifice must be divided in the ratio of the sacrifice amounts. We compute each partner’s sacrifice as “old share − new share.”Given Data / Assumptions:Old ratio A : B = 4 : 7 ⇒ A_old = 4/11, B_old = 7/11.New ratio with C = 1/3 each ⇒ A_new = B_new = 1/3.Premium = ₹ 2,20,000 split between A and B in the ratio of sacrifice.Concept / Approach: Sacrifice_A = A_old − A_new; Sacrifice_B = B_old − B_new. Divide the premium in Sacrifice_A : Sacrifice_B. Simplify the fraction ratio carefully.Step-by-Step Solution:Sacrifice_A = 4/11 − 1/3 = (12 − 11)/33 = 1/33.Sacrifice_B = 7/11 − 1/3 = (21 − 11)/33 = 10/33.Sacrifice ratio (A : B) = 1 : 10.Verification / Alternative check: The larger sacrifice belongs to B (from 7/11 down to 1/3), which aligns with the 1 : 10 split favoring B’s compensation.Why Other Options Are Wrong: 10 : 1 reverses the sacrifice; 9 : 10 and 10 : 9 do not match exact fractional differences; 4 : 7 is the old capital ratio, not the sacrifice ratio.Common Pitfalls: Using “new − old” instead of “old − new” for sacrifice or dividing the premium by old capital ratio instead of by the sacrifice ratio.Final Answer: 1 : 10

Question 10

Profit split with equal time but unequal capitals: P and Q invest ₹ 13,000 and ₹ 25,000, respectively, for 3 years. If the total profit is ₹ 76,000, what is Q’s share?

Accepted Answer

Introduction / Context: When partners keep their investments for the same duration, profit splitting reduces to the ratio of capitals alone. We simply apply the capital ratio to the total profit to find each person’s share accurately and quickly.Given Data / Assumptions:P capital = ₹ 13,000; Q capital = ₹ 25,000.Time = same for both (3 years), so it cancels in ratios.Total profit = ₹ 76,000.Concept / Approach: Profit share P : Q = 13,000 : 25,000 = 13 : 25. Q’s fraction of profit = 25 / (13 + 25) = 25/38. Multiply this fraction by the total profit to get Q’s amount.Step-by-Step Solution:Q share = 76,000 * (25/38).76,000 / 38 = 2,000 ⇒ Q share = 2,000 * 25 = ₹ 50,000.Verification / Alternative check: P share = 76,000 − 50,000 = ₹ 26,000, which matches 13/38 of the total profit, confirming correctness.Why Other Options Are Wrong: ₹ 26,000 is P’s share; other options do not match the 13 : 25 capital split with a total of ₹ 76,000.Common Pitfalls: Forgetting to add ratio parts before division or attempting to use time weights even though the time is the same for both partners.Final Answer: ₹ 50000

Question 11

Profit share proportional to capitals (same duration): Rajan and Sajan invest ₹ 14,200 and ₹ 15,600, respectively, for the whole year. If the total profit is ₹ 74,500, find Rajan’s share.

Accepted Answer

Introduction / Context: With equal investment periods, the profit share is simply proportional to the invested capitals. Compute Rajan’s fraction as his capital divided by the total capital, then multiply by the total profit to get his share.Given Data / Assumptions:Rajan = ₹ 14,200; Sajan = ₹ 15,600.Total profit = ₹ 74,500.Duration is the same for both.Concept / Approach: Rajan’s fraction = 14,200 / (14,200 + 15,600) = 14,200 / 29,800 = 71 / 149. Multiply this by the total profit to get the exact amount.Step-by-Step Solution:Total capital = 29,800; Rajan’s fraction = 71/149.Since 74,500 / 149 = 500, Rajan’s share = 500 * 71 = ₹ 35,500.Verification / Alternative check: Sajan’s share = 74,500 − 35,500 = ₹ 39,000. The ratio 35,500 : 39,000 reduces to 71 : 78 = 14,200 : 15,600, confirming correctness.Why Other Options Are Wrong: ₹ 39,600 and ₹ 39,000 refer to Sajan’s side or rounding errors; ₹ 35,000 and ₹ 36,000 do not match the precise fraction 71/149 applied to ₹ 74,500.Common Pitfalls: Approximating the fraction instead of using the exact division; losing precision leads to incorrect rupee amounts.Final Answer: ₹ 35500

Question 12

Three partners with fractional capital-time contributions: A invests 1/6 of capital for 1/6 of the total time; B invests 1/3 of capital for 1/3 of the time; C invests the remaining capital for the whole time. If the total profit is ₹ 4,600, find B’s…

Accepted Answer

Introduction / Context: When each partner invests a fraction of the total capital for a fraction of the total time, compute the effective contribution as (capital fraction * time fraction). The profit split is proportional to these effective contributions. Then multiply by total profit to get each share.Given Data / Assumptions:A: capital 1/6 for time 1/6 ⇒ weight = 1/36.B: capital 1/3 for time 1/3 ⇒ weight = 1/9.C: remaining capital = 1 − 1/6 − 1/3 = 1/2 for full time ⇒ weight = 1/2.Total profit = ₹ 4,600.Concept / Approach: Convert fractional weights to a common denominator to read integer parts and compute B’s fraction of the total. Then multiply by the total profit for the rupee amount.Step-by-Step Solution:Weights as parts on denominator 36: A = 1, B = 4, C = 18 ⇒ total parts = 23.B’s fraction = 4/23; B’s share = 4,600 * (4/23) = ₹ 800.Verification / Alternative check: A’s share = 4,600 * (1/23) = ₹ 200; C’s share = 4,600 * (18/23) = ₹ 3,600; sum = 200 + 800 + 3,600 = ₹ 4,600, confirming correctness.Why Other Options Are Wrong: ₹ 1,000, ₹ 960, ₹ 900, ₹ 650 correspond to incorrect weights or arithmetic errors with denominators.Common Pitfalls: Forgetting that C holds the remaining capital (1/2) and is in for the full time; or using sums of fractions incorrectly.Final Answer: Rs. 800

Question 13

Changing investments after a year adjusts the ratio: A, B, C initially invest in the ratio 3 : 5 : 7. After one year, C adds ₹ 3,37,600 and A withdraws ₹ 45,600. The new investment ratio becomes 24 : 59 : 167. Find A’s initial investment.

Accepted Answer

Introduction / Context: This problem links an initial ratio to a later ratio after specific additions and withdrawals. Express the initial amounts with a single variable and transform them as described. Equate each transformed amount to the corresponding part of the new ratio to solve for the variable and hence the exact initial figure requested.Given Data / Assumptions:Initial A : B : C = 3x : 5x : 7x.After 1 yr: A → 3x − 45,600; B → 5x; C → 7x + 3,37,600.New ratio = 24 : 59 : 167.Concept / Approach: Set 3x − 45,600 = 24k, 5x = 59k, 7x + 3,37,600 = 167k for some k. Solve from the cleanest equation 5x = 59k first, then substitute into the others to determine k and x consistently.Step-by-Step Solution:From 5x = 59k ⇒ x = 59k/5.Substitute into 3x − 45,600 = 24k ⇒ (177k/5) − 45,600 = 24k.Multiply by 5: 177k − 2,28,000 = 120k ⇒ 57k = 2,28,000 ⇒ k = 4,000.x = 59*4,000 / 5 = 47,200 ⇒ A_initial = 3x = ₹ 1,41,600.Verification / Alternative check: Check with C: 7x + 3,37,600 = 3,30,400 + 3,37,600 = 6,68,000; and 167k = 167 * 4,000 = 6,68,000, consistent.Why Other Options Are Wrong: Other values do not satisfy all three new-ratio equations simultaneously after substitutions.Common Pitfalls: Solving only two of the three equations or using addition in the wrong direction (e.g., adding instead of subtracting for A).Final Answer: Rs. 1,41,600

Question 14

Back-calculating a partner’s capital from a claimed profit share: A invests ₹ 16,000 for 8 months. B stays in the business for 4 months and claims 2/7 of the total profit. Find B’s capital.

Accepted Answer

Introduction / Context: With two partners, profit shares are proportional to capital × time. If a partner’s profit fraction is known, we can set up a ratio equation between the two capital-time products and solve for the unknown capital directly.Given Data / Assumptions:A capital = ₹ 16,000 for 8 months ⇒ A weight = 1,28,000.B time = 4 months; capital = y (unknown) ⇒ B weight = 4y.B’s profit fraction = 2/7 ⇒ A’s fraction = 5/7 ⇒ A : B = 5 : 2.Concept / Approach: Set the weight ratio equal to 5 : 2 and solve for y. This ensures the shares align with the claimed profit fraction exactly.Step-by-Step Solution:A : B = 1,28,000 : 4y = 5 : 2.1,28,000 / (4y) = 5/2 ⇒ 1,28,000 * 2 = 5 * 4y ⇒ 2,56,000 = 20y ⇒ y = ₹ 12,800.Verification / Alternative check: B weight = 4 * 12,800 = 51,200; ratio 1,28,000 : 51,200 = 5 : 2 (divide by 25,600), matching the profit claim.Why Other Options Are Wrong: ₹ 13,600, ₹ 11,900, ₹ 10,500, ₹ 14,000 do not maintain the 5 : 2 weight ratio with A’s 1,28,000 weight.Common Pitfalls: Using 2 : 5 instead of 5 : 2 for A : B, or forgetting to multiply capital by months to form weights.Final Answer: 12800

Question 15

Comparing profit shares after staggered changes and a late entrant: A invests ₹ 16,000; B invests ₹ 12,000. After 3 months, A withdraws ₹ 5,000 (so ₹ 11,000 thereafter), B adds ₹ 5,000 (so ₹ 17,000 thereafter). After another 3 months (at month 6), C…

Accepted Answer

Introduction / Context: This advanced partnership problem involves multiple changes in capitals over time and a new partner joining mid-year. The correct approach is to compute each partner’s money-months by segments and then apply proportional sharing of the total profit. Finally, compare B’s and C’s rupee shares.Given Data / Assumptions:Months 0–3: A = ₹ 16,000; B = ₹ 12,000; C = ₹ 0.Months 3–6: A = ₹ 11,000; B = ₹ 17,000; C = ₹ 0.Months 6–12: A = ₹ 11,000; B = ₹ 17,000; C = ₹ 21,000.Total profit = ₹ 26,400.Concept / Approach: Compute money-months for each partner by summing capital × months over segments, form total weights, and multiply the total profit by each partner’s weight fraction to obtain their shares. The required answer is B’s share minus C’s share.Step-by-Step Solution:A weight = (16,000*3) + (11,000*9) = 48,000 + 99,000 = 1,47,000.B weight = (12,000*3) + (17,000*9) = 36,000 + 1,53,000 = 1,89,000.C weight = (21,000*6) = 1,26,000.Total weight = 1,47,000 + 1,89,000 + 1,26,000 = 4,62,000.B share = 26,400 * (1,89,000 / 4,62,000) = 26,400 * (9/22) = ₹ 10,800.C share = 26,400 * (1,26,000 / 4,62,000) = 26,400 * (3/11) = ₹ 7,200.Difference = ₹ 10,800 − ₹ 7,200 = ₹ 3,600.Verification / Alternative check: A share = 26,400 − (10,800 + 7,200) = ₹ 8,400. The ratio 8,400 : 10,800 : 7,200 reduces to 7 : 9 : 6, which matches 1,47,000 : 1,89,000 : 1,26,000 after dividing by 21,000.Why Other Options Are Wrong: ₹ 1,200, ₹ 2,400, ₹ 4,800, and ₹ 3,000 do not follow from the exact weight fractions and produce inconsistencies with the total profit.Common Pitfalls: Forgetting to break the year into segments; misplacing when C joins; or using average capitals rather than exact segment sums.Final Answer: Rs. 3600

Question 16

Partnership profit sharing with staggered investments: Kanti starts a business by investing ₹ 90,000 for the entire year. After 5 months, Sudhakar joins by investing ₹ 80,000 (assume ₹ 80,000 as the intended figure under the recovery-first policy, s…

Accepted Answer

Introduction / Context: This partnership question tests the idea of capital-time weighting. When partners invest different amounts for different durations, profit is divided in the ratio of (capital * time). We also apply the recovery-first policy to interpret Sudhakar's amount as ₹ 80,000, which gives a clean and solvable ratio consistent with the provided options.Given Data / Assumptions: Kanti invests ₹ 90,000 for 12 months.Sudhakar invests ₹ 80,000 for 7 months (he joins after 5 months, so invests for 12 − 5 = 7 months).Total profit = ₹ 6,970.Profits are shared in proportion to capital * time.Concept / Approach: Profit share ratio = (Capital * Months of investment). Then each partner's share = (individual weight / total weight) * total profit.Step-by-Step Solution: Kanti's weight = 90,000 * 12 = 1,080,000. Sudhakar's weight = 80,000 * 7 = 560,000. Ratio = 1,080,000 : 560,000 = 27 : 14. Total parts = 27 + 14 = 41. Sudhakar's share = (14/41) * 6,970 = 14 * 170 = ₹ 2,380.Verification / Alternative check: Because 6,970 / 41 = 170 exactly, multiplying by 14 gives ₹ 2,380, which matches an option and validates the ratio-based approach.Why Other Options Are Wrong: ₹ 3,690 and ₹ 3,864 assume different weights; ₹ 1,883.73 implies a fractional ratio not arising from integer months; ₹ 2,170 does not match 14/41 of ₹ 6,970.Common Pitfalls: Forgetting to multiply capital by months, using 5 months for Sudhakar instead of 7, or dividing by the wrong total of parts.Final Answer: ₹ 2,380

Question 17

Two partners A and B invest in the ratio 3 : 2. If 5% of the total profit is donated to charity and A's actual share after donation is ₹ 855, what is the total profit before charity?

Accepted Answer

Introduction / Context: Partnership questions frequently include a charity deduction before the remaining amount is shared by ratio. You must apply the donation first and then split the remainder according to the investment ratio.Given Data / Assumptions: A : B = 3 : 2.Charity = 5% of total profit P.A's received amount after charity = ₹ 855.Concept / Approach: After donating 5%, the distributable amount is 95% of P (i.e., 0.95 * P). A's share is 3/5 of the distributable amount because A has 3 parts out of total 3 + 2 = 5 parts.Step-by-Step Solution: Distributable = 0.95 * P. A's amount = (3/5) * 0.95 * P = 0.57 * P. Given 0.57 * P = 855 ⇒ P = 855 / 0.57 = ₹ 1,500.Verification / Alternative check: 5% of 1,500 is 75. Remaining 1,425 shared 3:2 ⇒ A gets 855 and B gets 570. Matches the given condition.Why Other Options Are Wrong: Values other than ₹ 1,500 do not produce A's net share of ₹ 855 after charity when the 3 : 2 split is applied.Common Pitfalls: Splitting the entire profit without deducting charity or taking 3/5 of the total instead of 3/5 of the remaining 95%.Final Answer: ₹ 1,500

Question 18

Sanjay and Komal each invest ₹ 15,000 to start a business. After 8 months, Komal withdraws ₹ 10,000, leaving ₹ 5,000 invested for the remaining 4 months. If the annual profit is ₹ 32,000, what is Sanjay's share?

Accepted Answer

Introduction / Context: When partners change their capital mid-year, profit shares must reflect capital-time products (capital multiplied by months invested). This ensures fairness based on both amount and duration.Given Data / Assumptions: Sanjay: ₹ 15,000 for 12 months.Komal: ₹ 15,000 for 8 months, then ₹ 5,000 for 4 months.Total profit = ₹ 32,000.Concept / Approach: Compute each partner's capital-time weight and divide the profit proportionally.Step-by-Step Solution: Sanjay's weight = 15,000 * 12 = 180,000. Komal's weight = (15,000 * 8) + (5,000 * 4) = 120,000 + 20,000 = 140,000. Ratio = 180,000 : 140,000 = 18 : 14 = 9 : 7. Total parts = 16; Sanjay's fraction = 9/16. Sanjay's share = (9/16) * 32,000 = ₹ 18,000.Verification / Alternative check: Komal's share would be 7/16 of 32,000 = ₹ 14,000. The two shares sum to ₹ 32,000, consistent with the total profit.Why Other Options Are Wrong: ₹ 18,500, ₹ 17,000, and ₹ 16,500 do not fit the 9 : 7 split; ₹ 16,000 corresponds to an 8 : 8 equal split, which is not the case.Common Pitfalls: Ignoring Komal's changed capital in the last four months or dividing the profit only by the initial ratio.Final Answer: ₹ 18,000

Question 19

A is the working partner and B is the sleeping partner. A invests ₹ 12,000 and B invests ₹ 20,000. A receives 10% of the profit as a managing commission, and the remainder is divided in the ratio of their capitals. If the total profit is ₹ 9,600, ho…

Accepted Answer

Introduction / Context: Mixed distribution rules are common in partnership questions: a fixed percentage to the managing partner first, with the balance divided according to capital ratios. The order matters.Given Data / Assumptions: Total profit = ₹ 9,600.Managing commission to A = 10% of total profit.Remaining profit split by capital ratio 12,000 : 20,000 = 3 : 5.Concept / Approach: First take 10% of total for A. Then divide the remainder in 3 : 5, add A's two components to get the total received by A.Step-by-Step Solution: Commission to A = 10% of 9,600 = ₹ 960. Remainder = 9,600 − 960 = ₹ 8,640. A's share of remainder = 3/8 of 8,640 = ₹ 3,240. Total to A = 960 + 3,240 = ₹ 4,200.Verification / Alternative check: B's share of the remainder = 5/8 of 8,640 = ₹ 5,400; combined with A's 4,200 gives the full ₹ 9,600.Why Other Options Are Wrong: ₹ 3,240 and ₹ 3,600 exclude the commission; ₹ 4,500 and ₹ 4,000 misuse the sequence or ratio.Common Pitfalls: Splitting the entire profit by the ratio first, or applying the 10% on the remainder instead of the total profit.Final Answer: ₹ 4,200

Question 20

Jagmohan, Rooplal, and Pandeyji rent a video cassette for one week for ₹ 350. They use it for 6 hours, 10 hours, and 12 hours, respectively. If rent is split in proportion to usage time, how much should Pandeyji pay?

Accepted Answer

Introduction / Context: When a shared rental cost is divided by usage, each person pays in direct proportion to the hours used. Total cost times the person's fraction of total hours gives the correct split.Given Data / Assumptions: Total rent = ₹ 350.Usage hours: Jagmohan 6, Rooplal 10, Pandeyji 12.Cost split proportional to hours.Concept / Approach: Compute total hours, find Pandeyji's fraction, then multiply by total rent.Step-by-Step Solution: Total hours = 6 + 10 + 12 = 28 hours. Pandeyji's fraction = 12/28 = 3/7. Pandeyji's share = (3/7) * 350 = ₹ 150.Verification / Alternative check: The other two shares: Jagmohan = (6/28)*350 = ₹ 75; Rooplal = (10/28)*350 = ₹ 125. Sum = 75 + 125 + 150 = ₹ 350.Why Other Options Are Wrong: ₹ 75 and ₹ 125 correspond to the other users. ₹ 135 and ₹ 120 do not match proportional division with 12/28.Common Pitfalls: Dividing equally or using the inverse of hours. The proportional method must match actual usage.Final Answer: ₹ 150

Partnership Questions

Questions

Practice smarter