Question 1

A and B invest ₹ 3,000 and ₹ 4,000, respectively. A also receives ₹ 10 per month as remuneration for running the business. The remaining profit is divided in the ratio of investments. If in one year A receives ₹ 390 in total, how much does B receive?

Accepted Answer

Introduction / Context: This is a two-stage distribution: first, a fixed monthly amount to A for management; second, a proportional split of the remaining profit. We must separate these carefully to find B's portion. Given Data / Assumptions: A's remuneration = ₹ 10 per month ⇒ ₹ 120 per year. A's total received = ₹ 390 (includes remuneration + share of remainder). Remainder is split in ratio 3,000 : 4,000 = 3 : 4. Concept / Approach: Deduct A's remuneration from A's total to get A's share from the remainder. Then back out the total remainder and compute B's share. Step-by-Step Solution: A's share from remainder = 390 − 120 = ₹ 270. Let remainder = T. A gets 3/7 of T = 270 ⇒ T = 270 * (7/3) = ₹ 630. Therefore, B gets 4/7 of T = (4/7)*630 = ₹ 360. Verification / Alternative check: A's total = remuneration 120 + share 270 = ₹ 390. Remainder 630 splits to 270 and 360; sums check. Why Other Options Are Wrong: ₹ 630 is the whole remainder, not B's share. ₹ 480, ₹ 380, and ₹ 540 do not follow the 3 : 4 split from the computed remainder. Common Pitfalls: Treating ₹ 390 as A's share of the remainder only or splitting the entire profit before subtracting the fixed remuneration. Final Answer: ₹ 360

Question 2

A starts with ₹ 4,000 for 12 months; B joins after 3 months with ₹ 8,000 for 9 months; C invests ₹ 20,000 but only for the last 2 months. At year end, profit is ₹ 16,800. How should the profit be divided among A, B, and C?

Accepted Answer

Introduction / Context: Different start times and durations require capital-time weights for each partner. Profit division then follows those weights. Given Data / Assumptions: A: 4,000 for 12 months. B: 8,000 for 9 months. C: 20,000 for 2 months. Total profit = ₹ 16,800. Concept / Approach: Compute weights: A = 4,000*12, B = 8,000*9, C = 20,000*2. Reduce to a simple ratio and split the profit accordingly. Step-by-Step Solution: A's weight = 48,000; B's weight = 72,000; C's weight = 40,000. Ratio = 48,000 : 72,000 : 40,000 = 6 : 9 : 5. Total parts = 6 + 9 + 5 = 20; each part = 16,800 / 20 = ₹ 840. Shares: A = 6*840 = ₹ 5,040; B = 9*840 = ₹ 7,560; C = 5*840 = ₹ 4,200. Verification / Alternative check: Sum = 5,040 + 7,560 + 4,200 = ₹ 16,800, confirming the division. Why Other Options Are Wrong: Options that swap roles or change one figure break the 6 : 9 : 5 ratio implied by the investment schedule. Common Pitfalls: Forgetting C invests only for 2 months, or mistakenly assuming all invested for the full year. Final Answer: A = ₹ 5,040, B = ₹ 7,560, C = ₹ 4,200

Question 3

P, Q, and R start a business. Twice P's capital equals thrice Q's capital, and Q's capital is four times R's capital. If the annual profit is ₹ 1,48,500, what is Q's share?

Accepted Answer

Introduction / Context: Translating chained relationships into a single ratio for three partners enables proportional profit sharing. Given Data / Assumptions: 2P = 3Q ⇒ P : Q = 3 : 2. Q = 4R ⇒ Q : R = 4 : 1. Annual profit = ₹ 1,48,500. Concept / Approach: Combine ratios so that all three are expressed together. Then use the total parts to find each share. Step-by-Step Solution: From 2P = 3Q, P : Q = 3 : 2. From Q : R = 4 : 1, let Q = 4k ⇒ P = (3/2)*Q = 6k and R = 1k. Thus P : Q : R = 6 : 4 : 1 (equivalent to 3 : 2 : 0.5 scaled by 2). Total parts = 6 + 4 + 1 = 11. Q's fraction = 4/11. Q's share = (4/11) * 1,48,500 = ₹ 54,000. Verification / Alternative check: Remaining profit for P and R sums to 7/11 of 1,48,500 = ₹ 94,500, consistent with the partition. Why Other Options Are Wrong: They correspond to incorrect combined ratios or arithmetic with the fraction 4/11. Common Pitfalls: Writing P : Q as 2 : 3 or missing the step to link Q with R correctly. Final Answer: ₹ 54,000

Question 4

M, N, and P together invest ₹ 50,000. M invests ₹ 4,000 more than N, and N invests ₹ 5,000 more than P. If the total profit is ₹ 70,000, what is M's share of the profit?

Accepted Answer

Introduction / Context: When absolute differences among investments are given with a known total, solve for each capital first. Profit then divides proportional to those capitals (assuming equal time). Given Data / Assumptions: Total capital = ₹ 50,000. Let P = x; N = x + 5,000; M = x + 9,000. Total profit = ₹ 70,000; time equal for all. Concept / Approach: Solve 3x + 14,000 = 50,000 to find x, then compute the ratio M : N : P and apply it to the profit. Step-by-Step Solution: 3x + 14,000 = 50,000 ⇒ 3x = 36,000 ⇒ x = 12,000. P = 12,000; N = 17,000; M = 21,000. Ratio = 21,000 : 17,000 : 12,000. Total = 50,000; M's fraction = 21,000/50,000 = 0.42. M's share = 0.42 * 70,000 = ₹ 29,400. Verification / Alternative check: N's share would be 0.34 * 70,000 = ₹ 23,800 and P's share 0.24 * 70,000 = ₹ 16,800; totals match ₹ 70,000. Why Other Options Are Wrong: They do not reflect the 21:17:12 split derived from the constraints. Common Pitfalls: Misreading who invested more than whom, or assuming equal shares without using the capital differences. Final Answer: ₹ 29,400

Question 5

P, Q, and R hire a meadow for ₹ 2,920. P grazes 10 cows for 20 days, Q grazes 30 cows for 8 days, and R grazes 16 cows for 9 days. If rent is proportional to (cows × days), how much rent should R pay?

Accepted Answer

Introduction / Context: Shared rentals in grazing problems are allocated proportional to the product of the number of animals and the duration. Compute each party's usage weight and distribute the total cost accordingly. Given Data / Assumptions: P: 10 cows × 20 days = 200 cow-days. Q: 30 cows × 8 days = 240 cow-days. R: 16 cows × 9 days = 144 cow-days. Total rent = ₹ 2,920. Concept / Approach: R's share = (R's cow-days / total cow-days) * total rent. Step-by-Step Solution: Total cow-days = 200 + 240 + 144 = 584. R's fraction = 144/584 = 18/73 after dividing by 8. R's rent = (18/73) * 2,920 = 40 * 18 = ₹ 720 (since 2,920/73 = 40). Verification / Alternative check: P's and Q's portions similarly sum with R's to ₹ 2,920, reinforcing proportional correctness. Why Other Options Are Wrong: ₹ 735, ₹ 820, ₹ 575 deviate from the precise 144/584 fraction; only ₹ 720 equals (18/73)*2,920. Common Pitfalls: Using cows + days instead of cows × days or failing to reduce the fraction cleanly. Final Answer: ₹ 720

Question 6

A, B, and C enter into partnership. A invests an amount a from the start. After 6 months, B invests 2a. After 8 months, C invests 3a. If the annual profit is ₹ 54,000, what is C's share?

Accepted Answer

Introduction / Context: Here, each partner's capital-time product happens to be equal, leading to equal profit shares. This occurs because later partners invest proportionally larger capitals for proportionally shorter times. Given Data / Assumptions: A: a for 12 months ⇒ 12a. B: 2a for (12 − 6) = 6 months ⇒ 12a. C: 3a for (12 − 8) = 4 months ⇒ 12a. Total profit = ₹ 54,000. Concept / Approach: Since all capital-time weights are 12a, profits are equal among A, B, and C. Divide the total profit by 3 to find each share. Step-by-Step Solution: Weights: A = 12a; B = 12a; C = 12a. Ratio = 1 : 1 : 1. Each share = 54,000 / 3 = ₹ 18,000. Verification / Alternative check: Any base a cancels because all three weights equal 12a. Thus equal sharing is robust. Why Other Options Are Wrong: Any amount other than ₹ 18,000 would violate the equal-weight conclusion. Common Pitfalls: Forgetting that partners who join later may have higher capitals to balance the shorter duration, resulting in equal weights. Final Answer: ₹ 18,000

Question 7

A, B, and C start a business. B's investment equals one-sixth of the total capital, and A's and C's investments are equal (they split the remaining equally). If the annual profit is ₹ 33,600, find the difference between the profits of B and C.

Accepted Answer

Introduction / Context: Profit shares are proportional to invested capital when time is equal. If one partner has a specified fraction of the total and the others share the remainder equally, the profit split mirrors those capital fractions. Given Data / Assumptions: Total capital = T. B = T/6. Remaining capital = 5T/6; A = C = (5T/6)/2 = 5T/12 each. Total profit = ₹ 33,600. Concept / Approach: Convert the fractions into a simple integer ratio for A : B : C and then compute profits. Finally, take the difference between B's and C's profits. Step-by-Step Solution: Capitals: A = 5T/12, B = T/6, C = 5T/12. Express over a common denominator 12: A = 5, B = 2, C = 5. Profit ratio = 5 : 2 : 5; total parts = 12. Each part = 33,600 / 12 = ₹ 2,800. B's profit = 2 * 2,800 = ₹ 5,600; C's profit = 5 * 2,800 = ₹ 14,000. Difference (C − B) = 14,000 − 5,600 = ₹ 8,400. Verification / Alternative check: A also earns ₹ 14,000; sum = 14,000 + 5,600 + 14,000 = ₹ 33,600. Why Other Options Are Wrong: The other differences correspond to incorrect ratios or miscomputations of the per-part profit. Common Pitfalls: Treating B as 1/3 or sharing the remaining capital incorrectly instead of dividing 5T/6 equally between A and C. Final Answer: ₹ 8,400

Question 8

A and B invest in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share is ₹ 4,275 after the donation, what is the total profit?

Accepted Answer

Introduction / Context: This is the same structure as earlier: remove charity first, then divide the remainder using the investment ratio, equating A's portion to the given value. Given Data / Assumptions: A : B = 3 : 2. Charity = 5% of total profit P. A's share after donation = ₹ 4,275. Concept / Approach: A's portion = (3/5) * 0.95 * P = 0.57P. Set equal to 4,275 and solve for P. Step-by-Step Solution: 0.57P = 4,275 ⇒ P = 4,275 / 0.57 = ₹ 7,500. Charity = 5% of 7,500 = ₹ 375; distributable = ₹ 7,125. A's share = 3/5 of 7,125 = ₹ 4,275 (checks). Verification / Alternative check: B's share = 2/5 of 7,125 = ₹ 2,850; total after charity = 4,275 + 2,850 = 7,125; adding charity returns ₹ 7,500. Why Other Options Are Wrong: They do not produce A's post-charity amount of ₹ 4,275 under the 3 : 2 split. Common Pitfalls: Taking 3/5 of P directly or forgetting to subtract charity before splitting. Final Answer: ₹ 7,500

Question 9

A and B invest in the ratio 4 : 3. If 9% of the total profit goes to charity and A's share is ₹ 1,196 after charity, what is the total profit?

Accepted Answer

Introduction / Context: Again, the donation is removed first. Then the remainder is split 4 : 3, and A's portion is equated to the given figure to reverse-compute the total profit. Given Data / Assumptions: A : B = 4 : 3. Charity = 9% of total P. A receives ₹ 1,196 of the remainder. Concept / Approach: A's fraction of the distributable remainder is 4/7. The remainder is 91% of P, i.e., 0.91P. So A gets (4/7)*0.91P. Step-by-Step Solution: (4/7)*0.91P = 1,196. 0.91 * (4/7) = 364/700 = 0.52 exactly. Thus 0.52P = 1,196 ⇒ P = 1,196 / 0.52 = ₹ 2,300. Verification / Alternative check: Charity = 9% of 2,300 = ₹ 207; remainder = 2,093; A's share = 4/7 of 2,093 = ₹ 1,196. Why Other Options Are Wrong: Only ₹ 2,300 satisfies the exact fraction 0.52P = 1,196. Common Pitfalls: Using 4/7 of the total profit or rounding the product 0.91 * (4/7) incorrectly. Final Answer: ₹ 2,300

Question 10

A, B, and C invest for time periods in the ratio 2 : 1 : 8. Their profits at the end are in the ratio 3 : 4 : 2. Find the ratio of their investments (capitals) A : B : C.

Accepted Answer

Introduction / Context: Profit ∝ capital * time. With time ratios given and profit ratios known, you can back out the capital ratio by dividing profit ratios by time ratios termwise. Given Data / Assumptions: Time ratio = 2 : 1 : 8; Profit ratio = 3 : 4 : 2. Concept / Approach: For each partner, capital ∝ profit / time. Apply this to all three and then simplify the results to obtain A : B : C. Step-by-Step Solution: A's capital ∝ 3 / 2 = 1.5. B's capital ∝ 4 / 1 = 4. C's capital ∝ 2 / 8 = 0.25. To clear decimals, multiply all by 4 ⇒ A : B : C = 6 : 16 : 1. Verification / Alternative check: Using these capitals with the given times: (6*2):(16*1):(1*8) = 12:16:8 = 3:4:2, which matches the profit ratio. Why Other Options Are Wrong: They do not reproduce the 3:4:2 profit ratio when multiplied by the time ratio 2:1:8. Common Pitfalls: Multiplying profit and time instead of dividing, or forgetting to scale to remove fractions. Final Answer: 6 : 16 : 1

Question 11

A and B invest ₹ 20,000 and ₹ 25,000, respectively. After 4 months, B leaves and C joins with ₹ 15,000 for the remaining 8 months. If the annual profit is ₹ 23,000, what is C's share?

Accepted Answer

Introduction / Context: Partners coming and going change time weights. Profit must be shared by capital-time products across the year. Given Data / Assumptions: A: 20,000 for 12 months. B: 25,000 for 4 months. C: 15,000 for 8 months. Total profit = ₹ 23,000. Concept / Approach: Compute weights for A, B, and C, convert to a simple ratio, then allocate profit accordingly. Step-by-Step Solution: A's weight = 20,000*12 = 2,40,000. B's weight = 25,000*4 = 1,00,000. C's weight = 15,000*8 = 1,20,000. Ratio = 12 : 5 : 6 (dividing by 20,000). Total parts = 23; each part = 23,000 / 23 = ₹ 1,000. C's share = 6 * 1,000 = ₹ 6,000. Verification / Alternative check: Shares: A = ₹ 12,000; B = ₹ 5,000; C = ₹ 6,000. Sum = ₹ 23,000, consistent. Why Other Options Are Wrong: They do not match the 12:5:6 weight split based on given durations. Common Pitfalls: Assuming all are invested for 12 months or forgetting that B leaves and C joins at specific times. Final Answer: ₹ 6,000

Question 12

A and B invest ₹ 35,000 and ₹ 20,000, respectively. After 5 months B leaves; C joins with ₹ 15,000 for the remaining 7 months. If the profit at year end is ₹ 84,125, what is B's share?

Accepted Answer

Introduction / Context: Unequal durations require capital-time weighting. Compute each partner's weight and then allocate profit exactly proportional to these weights. Given Data / Assumptions: A: 35,000 for 12 months. B: 20,000 for 5 months. C: 15,000 for 7 months. Total profit = ₹ 84,125. Concept / Approach: Form weights, reduce to an integer ratio, then multiply by per-part profit to find B's share. Step-by-Step Solution: A's weight = 35,000*12 = 4,20,000. B's weight = 20,000*5 = 1,00,000. C's weight = 15,000*7 = 1,05,000. Ratio = 84 : 20 : 21 (dividing by 5,000). Total parts = 125; per part = 84,125 / 125 = ₹ 673. B's share = 20 * 673 = ₹ 13,460. Verification / Alternative check: A's share = 84 * 673 = ₹ 56,532; C's share = 21 * 673 = ₹ 14,133; sum equals ₹ 84,125. Why Other Options Are Wrong: ₹ 14,133 belongs to C. ₹ 15,000 or ₹ 12,800 are not integer multiples of ₹ 673 with part count 20. Common Pitfalls: Rounding the per-part value prematurely or mishandling months for B and C. Final Answer: ₹ 13,460

Question 13

P and Q are partners. P invests ₹ 8,000 for 8 months. Q stays in the business for 4 months and claims 2/7 of the total profit. How much money did Q invest?

Accepted Answer

Introduction / Context: Profit shares are proportional to capital-time. Knowing Q's time and claimed fraction lets us solve for Q's capital by setting up a proportion equation. Given Data / Assumptions: P: 8,000 for 8 months ⇒ weight = 64,000. Q: q for 4 months ⇒ weight = 4q. Q's profit fraction = 2/7. Concept / Approach: If Q's fraction is 2/7, then 4q / (64,000 + 4q) = 2/7. Solve for q. Step-by-Step Solution: 7*(4q) = 2*(64,000 + 4q). 28q = 1,28,000 + 8q ⇒ 20q = 1,28,000 ⇒ q = ₹ 6,400. Verification / Alternative check: Weights become 64,000 and 25,600. Q's fraction = 25,600 / 89,600 = 0.2857… = 2/7. Correct. Why Other Options Are Wrong: Other amounts do not yield the exact 2/7 claim when substituted into the proportion. Common Pitfalls: Using 2/7 of 4 months instead of the fraction of total weight, or mixing up months and capital. Final Answer: ₹ 6,400

Question 14

A and B invest ₹ 3,000 and ₹ 4,000, respectively. A is paid ₹ 10 per month as remuneration for running the business; the remaining profit is split according to investments. If A receives ₹ 390 in total during the year, how much does B receive?

Accepted Answer

Introduction / Context: This is the same remuneration-then-split structure. Separate the manager's fixed amount from A's total, then allocate the remainder by the 3 : 4 investment ratio to find B's amount. Given Data / Assumptions: A's remuneration = ₹ 120 per year. A's total receipt = ₹ 390 ⇒ A's share from remainder = 390 − 120 = ₹ 270. Remainder divided in 3 : 4 between A and B. Concept / Approach: Let remainder = T. Then A's part = 3/7 * T = 270 ⇒ T = 630. Hence B gets 4/7 of T. Step-by-Step Solution: T = 270 * (7/3) = ₹ 630. B's share = (4/7) * 630 = ₹ 360. Verification / Alternative check: A total = 120 + 270 = ₹ 390; B = ₹ 360; remainder sum = 270 + 360 = 630, consistent. Why Other Options Are Wrong: They do not follow from the 3 : 4 split of the computed remainder. Common Pitfalls: Treating ₹ 390 as only A's split share or ignoring the fixed monthly remuneration. Final Answer: ₹ 360

Question 15

Amit and Brijesh invest in the ratio 12 : 11. Their annual profits are in the ratio 4 : 1. If Amit invested for 11 months, for how many months did Brijesh invest?

Accepted Answer

Introduction / Context: Profit is proportional to capital × time. Given the capital ratio and the profit ratio, we can determine the missing time of investment for Brijesh using a simple proportional equation. Given Data / Assumptions: Capitals: Amit : Brijesh = 12 : 11. Profits: Amit : Brijesh = 4 : 1. Amit's time = 11 months; Brijesh's time = t months (unknown). Concept / Approach: Since profit ∝ capital × time, set (12 * 11) : (11 * t) = 4 : 1 and solve for t. This uses the fact that the constant of proportionality cancels in the ratio. Step-by-Step Solution: Amit's weight = 12 * 11 = 132. Brijesh's weight = 11 * t. 132 : 11t = 4 : 1 ⇒ 132/(11t) = 4/1 ⇒ 132 = 44t ⇒ t = 3 months. Verification / Alternative check: With t = 3, Brijesh's weight = 33; Amit's weight = 132; ratio = 132 : 33 = 4 : 1 as required. Why Other Options Are Wrong: 9, 5, 10, 7 months do not satisfy 132 : 11t = 4 : 1. Common Pitfalls: Reversing the ratios or forgetting that profits scale with both capital and time, not just capital. Final Answer: 3 months

Question 16

Partnership with time-weighted capitals and a mid-year change: Amitabh, Brijesh, and Kamlesh begin a partnership with initial capital shares in the ratio 7/2 : 4/3 : 6/5, respectively. After 4 months, Amitabh increases his capital by 50% for the rem…

Accepted Answer

Introduction / Context: This partnership question tests the time-weighted capital concept. Profits are divided in the ratio of (capital * time). Since Amitabh increases his capital after 4 months, we must split his contribution into two time blocks and then compare with Brijesh and Kamlesh who keep their capitals unchanged throughout the year. Given Data / Assumptions: Initial capital ratio: Amitabh : Brijesh : Kamlesh = 7/2 : 4/3 : 6/5. Amitabh invests 7/2 units for the first 4 months, then increases by 50% to 21/4 units for the next 8 months. Brijesh invests 4/3 units for all 12 months. Kamlesh invests 6/5 units for all 12 months. Total profit = ₹ 21600. Concept / Approach: Compute each partner’s money–time product and use these as weights to split the profit. For Amitabh, compute two segments due to the 50% increase. For Brijesh and Kamlesh, multiply their capitals by 12 months directly. Step-by-Step Solution: Amitabh's weight = (7/2)*4 + (21/4)*8 = 14 + 42 = 56.Brijesh's weight = (4/3)*12 = 16.Kamlesh's weight = (6/5)*12 = 72/5 = 14.4.Total weight = 56 + 16 + 14.4 = 86.4.Brijesh's share = 21600 * (16 / 86.4) = 21600 * (1 / 5.4) ≈ 4000 (exactly 4000 since 86.4 * 250 = 21600). Verification / Alternative check: Since 86.4 × 250 = 21600, the per-weight share is 250. Brijesh has 16 weights, so 16 × 250 = ₹ 4000, which matches our computation precisely. Why Other Options Are Wrong: ₹ 8000 and ₹ 12000 are too large relative to Brijesh’s smaller weight compared to Amitabh. ₹ 7000 does not match the exact weight-based split. Common Pitfalls: Forgetting to split Amitabh’s capital into two time periods after his 50% increase. Dividing by simple capital ratios without multiplying by months. Final Answer: ₹ 4000

Question 17

Joint business with unequal capitals and times: A and B start a business. A’s capital is thrice B’s capital, and A keeps it invested for twice B’s time. If B’s profit share is ₹ 6000, what is 20% of the total profit?

Accepted Answer

Introduction / Context: In partnership problems, the profit share of each partner is proportional to the product of capital and time. Here, A’s capital is larger and invested longer, while we are given B’s final share. From this, we reconstruct the total and then find 20% of it. Given Data / Assumptions: A’s capital = 3 × B’s capital. A’s time = 2 × B’s time. Profit share ratio A : B = (3 × 2) : 1 = 6 : 1. B’s profit = ₹ 6000 (i.e., 1 part). Concept / Approach: If A : B = 6 : 1, then total parts = 7. Hence the total profit equals 7 times B’s share. Then take 20% of that total as required by the question. Step-by-Step Solution: Total profit = 7 × ₹ 6000 = ₹ 42000.Required = 20% of ₹ 42000 = 0.20 * 42000 = ₹ 8400. Verification / Alternative check: Check the internal split: A gets 6 × 6000 = ₹ 36000, B gets ₹ 6000; total ₹ 42000. Twenty percent of that is indeed ₹ 8400. Why Other Options Are Wrong: ₹ 5000, ₹ 3500, and ₹ 4500 are not 20% of ₹ 42000; thus they do not fit the derived total. Common Pitfalls: Treating capitals alone as the basis, ignoring the time factor. Multiplying B’s share by 20% directly without computing the total profit first. Final Answer: ₹ 8400

Question 18

Staggered investments and a new partner: A and B invest ₹ 16000 and ₹ 12000. After 3 months, A withdraws ₹ 5000 while B adds ₹ 5000. After 3 more months, C joins with ₹ 21000. At year-end, the profit is ₹ 13200. By how much does B’s share exceed C’s…

Accepted Answer

Introduction / Context: This partnership problem combines changing capitals over time and the entry of a new partner. The profit split must respect the money–time products across the distinct periods of the year. Given Data / Assumptions: Months 1–3: A = 16000, B = 12000. Months 4–6: A = 11000, B = 17000. Months 7–12: A = 11000, B = 17000, C = 21000. Total profit = ₹ 13200. Concept / Approach: Compute each partner’s weight = sum of (capital * months) over relevant periods. Then divide the profit proportionally. Finally, compute the excess of B’s share over C’s share. Step-by-Step Solution: A's weight = 16000*3 + 11000*3 + 11000*6 = 48000 + 33000 + 66000 = 147000.B's weight = 12000*3 + 17000*3 + 17000*6 = 36000 + 51000 + 102000 = 189000.C's weight = 21000*6 = 126000.Total weight = 147000 + 189000 + 126000 = 462000.Per-weight profit = 13200 / 462000 = 1/35.B's share = 189000 / 35 = ₹ 5400; C's share = 126000 / 35 = ₹ 3600.Difference = ₹ 5400 − ₹ 3600 = ₹ 1800. Verification / Alternative check: The weights reduce in the ratio 147 : 189 : 126 = 7 : 9 : 6. Total parts 22; profit per part = 13200/22 = 600. Then A = 7*600 = 4200, B = 9*600 = 5400, C = 6*600 = 3600; difference 1800, consistent. Why Other Options Are Wrong: ₹ 1600, ₹ 2100, and ₹ 2300 do not match the exact weight-based calculation. Common Pitfalls: Not splitting the year into correct 3–3–6 month blocks. Forgetting A’s withdrawal and B’s addition when computing later-period weights. Final Answer: ₹ 1800

Question 19

Profit split with partial equal division and interest on capital: Two partners invest ₹ 125000 and ₹ 85000. They agree that 60% of the profit is divided equally and the remaining 40% is distributed in the ratio of their capitals. If one partner rece…

Accepted Answer

Introduction / Context: This is a hybrid profit-sharing agreement: part equally, part proportional to capital (often called interest on capital). We use the difference between partners’ final receipts to back-solve the total profit. Given Data / Assumptions: Capitals: 125000 and 85000 → ratio 25 : 17. 60% of profit split equally; 40% split in 25 : 17. Difference between partners’ totals = ₹ 600. Concept / Approach: Let total profit be P. Each gets 0.3P from the equal part. From the 40% part, the first gets 0.4P*(25/42), the second 0.4P*(17/42). The difference equals 0.4P*(8/42) = (1.6/21)P. Set this equal to ₹ 600 and solve for P. Step-by-Step Solution: Difference = 0.4P * (25−17)/42 = 0.4P * 8/42 = (1.6/21)P.(1.6/21)P = 600 ⇒ P = 600 * 21 / 1.6 = 600 * 13.125 = ₹ 7875. Verification / Alternative check: Compute the unequal portion: 0.4P = 3150. Shares in 25 : 17 are 1875 and 1275, difference 600. The equal portion is 0.6P = 4725 → 2362.5 each. Totals differ by exactly 600, confirming P = ₹ 7875. Why Other Options Are Wrong: ₹ 8800, ₹ 8885, and ₹ 8995 do not satisfy the derived proportional difference. Common Pitfalls: Mistaking 60% as per-head rather than equal split. Using 25 : 17 on the whole profit instead of only the 40% portion. Final Answer: ₹ 7875

Question 20

A and B invest in a business in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share is Rs. 855, the total profit is :

Accepted Answer

Let the total profit be Rs. 100. After paying to charity, A's share = (95*3/5) = Rs. 57. If A's share is Rs. 57, total profit = Rs. 100. If A's share is Rs. 855, total profit = (100/57*855) = 1500.

Partnership Questions