Question 1

A, B and C invest in the ratio 7⁄2 : 4⁄3 : 6⁄5. After 4 months, A increases his investment by 50%. If the total profit after one year is Rs. 21,600, what is B's share?

Accepted Answer

Problem restatement Profits are proportional to (capital × time). A invests in two phases: first 4 months at his original capital; next 8 months at 1.5 times that capital. B and C keep their capitals constant for 12 months. Given data Capital ratios: A : B : C = 7⁄2 : 4⁄3 : 6⁄5 Time: total 12 months; A increases capital after 4 months by 50% Total profit = Rs. 21,600 Concept/Approach Convert fractional ratios to a common integer base and compute time-weighted contributions. Step-by-step calculation Choose base so that A = 105, B = 40, C = 36 (LCM of denominators 2,3,5 → 30; so 7⁄2=105⁄30, 4⁄3=40⁄30, 6⁄5=36⁄30)A's contribution = 4×A + 8×(1.5A) = 4A + 12A = 16A = 16×105 = 1680B's contribution = 12×B = 12×40 = 480C's contribution = 12×C = 12×36 = 432Total = 1680 + 480 + 432 = 2592B's profit share fraction = 480 ÷ 2592 = 5 ÷ 27B's profit = 21,600 × (5÷27) = Rs. 4,000 Verification/Alternative Fraction 5⁄27 ≈ 0.185185; 0.185185 × 21,600 = 4,000. Common pitfalls Multiplying A's capital by 1.5 for the full 12 months (the increase starts after 4 months only). Final Answer Rs. 4,000

Question 2

A starts a business with Rs. 3,500. After 5 months, B joins as a partner. After one year from the start, profits are shared in the ratio 2 : 3 (A : B). What is B's capital contribution?

Accepted Answer

Problem restatement Profit shares reflect capital × time. A invests for 12 months, B for the last 7 months. The final ratio A : B = 2 : 3. Find B's capital. Given data A's capital = 3,500 for 12 months ⇒ 3,500 × 12 B joins after 5 months ⇒ time = 7 months with capital = x Profit ratio = 2 : 3 (A : B) Concept/Approach Set the ratio of capital-months equal to 2 : 3 and solve for x. Step-by-step calculation A : B = (3,500 × 12) : (x × 7) = 2 : 342,000 : 7x = 2 : 3 ⇒ 42,000 × 3 = 7x × 2126,000 = 14x ⇒ x = 9,000 Verification/Alternative A's share units = 42,000; B's units with x = 9,000 → 63,000, giving 42,000 : 63,000 = 2 : 3. Common pitfalls Taking B's time as 12 months (he joined 5 months late). Final Answer Rs. 9,000

Question 3

A and B invest Rs. 20,000 and Rs. 15,000 respectively. After 6 months, C joins with Rs. 20,000. If the total profit at the end of 2 years from start is Rs. 25,000, what is B's share?

Accepted Answer

Problem restatement Compute profit shares via capital × time. A and B invest from the start; C enters after 6 months. The business runs for 24 months from the start. Given data A = 20,000 for 24 months ⇒ 480,000 units B = 15,000 for 24 months ⇒ 360,000 units C = 20,000 for 18 months ⇒ 360,000 units Total profit = Rs. 25,000 Concept/Approach Profit share = (partner's units) ÷ (total units) × total profit. Step-by-step calculation Total units = 480,000 + 360,000 + 360,000 = 1,200,000B's fraction = 360,000 ÷ 1,200,000 = 0.30B's profit = 0.30 × 25,000 = Rs. 7,500 Verification/Alternative Shares are proportional: A : B : C = 480 : 360 : 360 = 4 : 3 : 3; total parts = 10; B gets 3⁄10 of 25,000 = 7,500. Common pitfalls Using 24 months for C as well (C joined after 6 months; only 18 months counted). Final Answer Rs. 7,500

Question 4

Aman invests ₹70,000 from the start. Rakhi joins after 6 months with ₹1,05,000, and Sagar joins 6 months later with ₹1,40,000. If the profit is distributed 3 years after Aman started, in what ratio should Aman : Rakhi : Sagar share the profit?

Accepted Answer

Problem restatement Profits in partnerships are divided in proportion to capital × time. We are given different joining times over a total horizon of 3 years (36 months). Given data Aman: ₹70,000 invested for 36 months. Rakhi: ₹1,05,000 invested for 30 months (joins after 6 months). Sagar: ₹1,40,000 invested for 24 months (joins after another 6 months). Concept/Approach Profit shares are proportional to the product of amount invested and duration invested. Step-by-step calculation Aman's units = 70,000 × 36 = 25,20,000 Rakhi's units = 1,05,000 × 30 = 31,50,000 Sagar's units = 1,40,000 × 24 = 33,60,000 Divide all by 10,000 → 252 : 315 : 336 Simplify by 21 → 12 : 15 : 16 Verification/Alternative Check months: 36, 30, 24 correctly reflect 0, 6, 12-month join points across 36-month horizon. Common pitfalls Using only capital ratios and ignoring time weighting. Using 12 and 18 months for later partners (misreading the 6-month gaps). Final Answer 12 : 15 : 16

Question 5

A and B invest in the ratio 3 : 5. After 6 months, C joins with the same amount as B. At the end of one year, in what ratio should A : B : C share the profit?

Accepted Answer

Problem restatement Determine the profit-sharing ratio when partners invest different amounts and join at different times within a 1-year (12-month) period. Given data Capital ratio initially: A : B = 3x : 5x for 12 months. C joins after 6 months with capital equal to B, i.e., 5x for 6 months. Concept/Approach Profit share ∝ (capital × time). Step-by-step calculation A units = 3x × 12 = 36x B units = 5x × 12 = 60x C units = 5x × 6 = 30x Ratio = 36 : 60 : 30 = 6 : 10 : 5 Common pitfalls Forgetting that C's capital works only for 6 months. Final Answer 6 : 10 : 5

Question 6

Arun, Kamal, and Vinay invest ₹8,000, ₹4,000, and ₹8,000 respectively. Arun withdraws after 6 months. If the total profit after 8 months is ₹4,005, what is Kamal's share?

Accepted Answer

Problem restatement Compute each partner's time-weighted capital and then allocate the profit accordingly. Arun leaves at month 6; business ends at month 8. Given data Arun: ₹8,000 for 6 months. Kamal: ₹4,000 for 8 months. Vinay: ₹8,000 for 8 months. Total profit = ₹4,005. Concept/Approach Shares ∝ capital × time (money-months). Step-by-step calculation Arun units = 8,000 × 6 = 48,000 Kamal units = 4,000 × 8 = 32,000 Vinay units = 8,000 × 8 = 64,000 Ratio = 48,000 : 32,000 : 64,000 = 3 : 2 : 4 Sum of parts = 3 + 2 + 4 = 9 One part = 4,005 ÷ 9 = 445 Kamal's share = 2 × 445 = ₹890 Verification Arun's share = 3 × 445 = ₹1,335; Vinay's = 4 × 445 = ₹1,780; total = 1,335 + 890 + 1,780 = ₹4,005. Common pitfalls Dividing profit by the raw capital ratio without time-weighting. Final Answer ₹890

Question 7

A and B invest in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share of the remainder is ₹855, what is the total profit?

Accepted Answer

Problem restatement A fixed 5% of the total profit P is donated. The remaining 95% is divided between A and B in the ratio 3 : 2, with A's portion equal to ₹855. Find P. Given data Charity = 5% of P → distributable = 95% of P. A's share from distributable = (3/5) × 0.95P = ₹855. Concept/Approach Set up an equation for A's share and solve for P. Step-by-step calculation (3/5) × 0.95P = 0.57P = 855 P = 855 ÷ 0.57 = ₹1,500 Verification Distributable = 0.95 × 1,500 = ₹1,425. A's share = 3/5 × 1,425 = ₹855 (matches). Common pitfalls Applying 5% charity after taking A's share instead of before. Final Answer ₹1,500

Question 8

A, B, and C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months, and C puts 15 oxen for 3 months. If the total rent is ₹175, how much should C pay?

Accepted Answer

Problem restatement Rent is shared in proportion to oxen × months. Given data A: 10 × 7 = 70 ox-months. B: 12 × 5 = 60 ox-months. C: 15 × 3 = 45 ox-months. Total rent = ₹175. Concept/Approach Share ∝ ox-months. Step-by-step calculation Total ox-months = 70 + 60 + 45 = 175 C's fraction = 45/175 C's rent = 45/175 × ₹175 = ₹45 Final Answer ₹45

Question 9

A begins a business with ₹85,000. Later, B joins with ₹42,500. If year-end profits are shared in the ratio 3 : 1 (A : B), for how many months did B's capital remain invested?

Accepted Answer

Problem restatement Find B's joining duration given capitals and the final profit ratio over a 12-month year. Given data A: ₹85,000 for 12 months. B: ₹42,500 for t months. Profit ratio A : B = 3 : 1. Concept/Approach Profit share ∝ capital × time. Step-by-step calculation 85,000 × 12 : 42,500 × t = 3 : 1 10,20,000 : 42,500t = 3 : 1 10,20,000 ÷ (42,500t) = 3 ⇒ 10,20,000 = 1,27,500t t = 10,20,000 ÷ 1,27,500 = 8 months Final Answer 8 months

Question 10

A, B, C subscribe ₹50,000 in total. A invests ₹4,000 more than B, and B invests ₹5,000 more than C. If the total profit is ₹35,000, how much does A receive?

Accepted Answer

Problem restatement Find each person's capital from the given differences and the total capital, then allocate profit proportional to capital (assuming equal time). Given data Let C = x ⇒ B = x + 5,000 ⇒ A = x + 9,000. A + B + C = 50,000. Total profit = ₹35,000. Step-by-step calculation x + (x + 5,000) + (x + 9,000) = 50,000 3x + 14,000 = 50,000 ⇒ x = 12,000 C = 12,000, B = 17,000, A = 21,000 A's share = (21,000/50,000) × 35,000 = ₹14,700 Verification Shares sum correctly if computed similarly for B and C. Final Answer ₹14,700

Question 11

Three partners share profit in the ratio 5 : 7 : 8 for working periods of 14, 8, and 7 months respectively. What was the ratio of their investments?

Accepted Answer

Problem restatement Given profit shares and the months each partner remained invested, back out the ratio of investments. Concept/Approach Profit ∝ (investment × time). If I1, I2, I3 are investments and t1, t2, t3 their durations, then: I1t1 : I2t2 : I3t3 = 5 : 7 : 8 Thus, I1 : I2 : I3 = (5/14) : (7/8) : (8/7) Step-by-step calculation Multiply each by LCM(14, 8, 7) = 56: (5/14)×56 = 20 (7/8)×56 = 49 (8/7)×56 = 64 Investment ratio = 20 : 49 : 64 Common pitfalls Inverting time factors (dividing instead of multiplying by months). Final Answer 20 : 49 : 64

Question 12

A invests ₹6,500 for 6 months; B invests ₹8,400 for 5 months; C invests ₹10,000 for 3 months. A, as the working partner, receives 5% of the profit as remuneration. If total profit is ₹7,400, what is B's share?

Accepted Answer

Problem restatement First allocate 5% of the profit to the working partner (A). Distribute the remaining profit in the ratio of capital × time among A, B, C. Compute B's amount. Given data Total profit = ₹7,400. Working partner (A) gets 5% = ₹370. Distributable remainder = ₹7,400 − ₹370 = ₹7,030. Capital-months: A: 6,500 × 6 = 39,000 B: 8,400 × 5 = 42,000 C: 10,000 × 3 = 30,000 Concept/Approach Shares of the remainder are proportional to 39,000 : 42,000 : 30,000 = 13 : 14 : 10. Step-by-step calculation Total parts = 13 + 14 + 10 = 37 Each part = 7,030 ÷ 37 = 190 B's share = 14 × 190 = ₹2,660 Verification A's and C's shares of the remainder are 13×190 = ₹2,470 and 10×190 = ₹1,900 respectively. Adding A's remuneration: A gets ₹2,470 + ₹370 = ₹2,840; totals sum to ₹7,400. Final Answer ₹2,660

Question 13

A and B invest in the ratio 4 : 5. After 3 months, A withdraws 1/4 of his capital and B withdraws 1/5 of his capital. If the total profit at the end of 10 months is ₹760, what is A's share?

Accepted Answer

Problem restatement Capitals change once during the year. Use time-weighted capitals to split the profit. Given data Initial capitals: A = 4k, B = 5k. After 3 months: A withdraws 1/4 ⇒ new A = 3k; B withdraws 1/5 ⇒ new B = 4k. Total period = 10 months. Concept/Approach Compute capital-months before and after the change. Step-by-step calculation First 3 months: A = 4k × 3 = 12k; B = 5k × 3 = 15k Next 7 months: A = 3k × 7 = 21k; B = 4k × 7 = 28k Totals: A = 12k + 21k = 33k; B = 15k + 28k = 43k Profit ratio A : B = 33 : 43 A's share = ₹760 × (33/(33+43)) = 760 × (33/76) = ₹330 Verification 760 ÷ 76 = 10; 10 × 33 = ₹330 (A), remainder ₹430 (B). 330 : 430 = 33 : 43. Common pitfalls Splitting by initial 4 : 5 ratio without time adjustments after withdrawals. Final Answer ₹330

Question 14

Simran invests Rs. 50,000 to start a software business. After 6 months, Nanda joins with Rs. 80,000. After 3 years, the profit is Rs. 24,500. What is Simran's share of the profit?

Accepted Answer

Problem restatement Profits in a partnership are divided in proportion to (capital × time). Simran invests first; Nanda joins after 6 months. Compute time-weighted capitals and apportion the total profit. Given data Simran's capital = Rs. 50,000 for 3 years. Nanda's capital = Rs. 80,000 for 2.5 years (joins after 6 months). Total profit = Rs. 24,500. Concept/Approach Use capital–month (or capital–year) products to get their profit-sharing ratio, then apply the ratio to the total profit. Step-by-Step calculation Simran's units = 50,000 × 3 = 150,000Nanda's units = 80,000 × 2.5 = 200,000Ratio (Simran : Nanda) = 150,000 : 200,000 = 3 : 4Total parts = 3 + 4 = 7Simran's share = (3/7) × 24,500 = 10,500 Verification/Alternative If Nanda had also invested for 3 years, the ratio would be 5:8; reducing Nanda's time to 2.5 years scales her part to 4 and yields 3:4 overall—consistent. Common pitfalls Using plain capital ratio (50,000:80,000) without accounting for different investment durations. Final Answer Rs. 10,500

Question 15

Pramod started a business with Rs. 40000. After 4 months Vikas also joined him with Rs. 60000. If at the end of the year, the profit is Rs. 16000, what is the share of Vikas in the profit?

Accepted Answer

Ratio between the investment of Pramod and Vikas = 40000 x 12 : 60000 x 8 = 480000 : 480000 = 1 : 1 Total profit = Rs. 16000 share of Vikas in profit = 16000/2 = Rs. 8,000

Question 16

A and B start a business with initial investment in the ratio 12 : 11 and their annual profits were in the ratio 4 : 1. If A invested the money for 11 months . B invested the money for?

Accepted Answer

Suppose B invested the money for N months. Then the ratio of investment = (12 x 11 : 11 x N) = 12 : N ∴ 12/N = 4/1 ⇒ N = 3 months.

Question 17

A and B started a joint firm. A's investment was thrice the investment of B and the period of his investment was two times the period of investment of B. If B got Rs. 4,000 as profit then their total profit is?

Accepted Answer

Suppose B invested Rs. x for y months. Then A's investment is Rs. 3x for 2y months. Ratio of investment of A and B = 6xy : xy = 6 : 1. Now B's share = Rs. 4,000 ∴ A's share = Rs. 24, 000 Hence, Total profit = Rs. 28,000

Question 18

Dilip, Ram and Amar started a shop by investing Rs. 27,000, Rs. 81,000 and Rs. 72,000 respectively. At the end of one year the profit was distributed. If Ram's share of profit be Rs. 36,000, then the total profit was?

Accepted Answer

Ratio of shares = 27000 : 81000 : 72000 = 3 : 9 : 8 If Ram's share is Rs. 9 then total profit = Rs. 20 If Ram's share is Rs. 36000 then total profit = Rs. (20/9) x 36000 = Rs. 80000

Question 19

Rs. 700 is dividing among A, B and C so that A receives half as much as B and B half as much as C. Then C's share is?

Accepted Answer

Let C's share = Rs. N Then B's share = Rs. N/2 and A's share = Rs. N/4 ∴ A : B : C = N/4 : N/2 : N = 1 : 2 : 4 Hence C's share = Rs. 700 x (4/7) = Rs. 400

Question 20

Jayant started a business, investing Rs. 6000. Six months later Madhu joined him, investing Rs. 4000. If they made a profit of Rs. 5200 at the end of the year. How much must be the share of Madhu?

Accepted Answer

Ratio of their shares = (6000 x 12) : (4000 x 6) = 3 : 1 ∴ Madhu's share = Rs.5200 x (1/4)

Partnership Questions