Question 1

Two businessmen A and B invest in a business in the ratio 5 : 8. They decide that 30% of the total profit will be reinvested into the business and only the remaining 70% will be distributed between them in the same ratio. If A's share of the distrib…

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Introduction / Context:This problem is based on a simple partnership scenario where two partners share profit in a fixed ratio but also choose to reinvest a part of the profit back into the business. The key idea is distinguishing between total profit and the portion that is actually distributed to the partners. Understanding this distinction and handling percentage and ratio calculations correctly is essential for solving such questions commonly asked in quantitative aptitude exams. Given Data / Assumptions:- Two partners A and B invest in the ratio 5 : 8.- Let total profit be P rupees.- 30% of the total profit is reinvested in the business.- Therefore, 70% of the total profit is distributed among A and B.- The distributed portion is shared in the ratio 5 : 8.- A's share from the distributed profit is Rs. 87,500.- We are required to find the total profit P. Concept / Approach:The approach involves two layers of proportional reasoning. First, only 70% of the profit is available for distribution. Second, that 70% is divided between A and B according to their capital ratio of 5 : 8. The share received by A is therefore a fixed fraction of the total profit. By expressing A's share in terms of P and equating it to Rs. 87,500, we can solve a simple linear equation to obtain the value of P. Step-by-Step Solution:Step 1: Let total profit be P.Step 2: Reinvestment is 30% of P, so distributed profit = 70% of P.Step 3: Therefore, distributed profit = 0.70 * P.Step 4: This distributed amount is shared in the ratio 5 : 8, so total ratio parts = 5 + 8 = 13.Step 5: A's share = (5 / 13) of the distributed profit.Step 6: Hence, A's share = (5 / 13) * 0.70 * P.Step 7: Note that 0.70 = 7 / 10, so A's share = (5 / 13) * (7 / 10) * P = (35 / 130) * P = (7 / 26) * P.Step 8: We are given A's share = Rs. 87,500, so (7 / 26) * P = 87,500.Step 9: Solve for P: P = 87,500 * (26 / 7).Step 10: 87,500 * 26 = 2,275,000 and dividing by 7 gives P = 325,000.Therefore, the total profit is Rs. 3,25,000. Verification / Alternative check:Take P = 325,000.Distributed profit = 70% of 325,000 = 0.70 * 325,000 = 227,500.A's share = (5 / 13) * 227,500.Compute: 227,500 / 13 = 17,500 and 17,500 * 5 = 87,500.This matches the given information, so the result is consistent. Why Other Options Are Wrong:- 227000: This is close to the distributed profit, not the total profit, and ignores the reinvested portion.- 250000: This would give a smaller distributed amount and therefore a smaller share for A than 87,500.- 375000: This would produce an A share larger than 87,500 if calculated correctly, so it does not fit the data. Common Pitfalls:- Treating Rs. 87,500 as A's share out of the entire profit rather than from the 70% portion.- Using the ratio 5 : 8 directly on the total profit P instead of on the distributed profit only.- Mistakes in handling percentages, especially not converting 30% reinvestment into 70% distribution correctly.- Arithmetic errors when solving (7 / 26) * P = 87,500. Final Answer:The total profit earned by the business was Rs. 3,25,000.

Question 2

A and B start a partnership business with initial investments in the ratio 5 : 6. After 6 months, C joins them by investing an amount equal to two-thirds of B's capital. At the end of the year, C's share of the profit is Rs. 21,600. What is the tota…

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Introduction / Context:This partnership question deals with different joining times and different capital amounts. It focuses on the concept that profit in a partnership is divided in proportion to the product of capital and time, often called money-months or money-time units. Here, A and B start the business together, while C joins later with a specific fraction of B's capital. Based on C's known share of profit, we must work backwards to determine the total profit. Such questions are common in aptitude tests and help reinforce the idea of weighted contributions over time. Given Data / Assumptions:- A and B invest in the ratio 5 : 6.- Let B's capital be 6x; then A's capital is 5x.- C joins after 6 months with capital equal to two-thirds of B's capital.- Thus, C's capital is (2/3) * 6x = 4x.- Total business duration is 12 months from the start.- A and B remain invested for 12 months, C for 6 months.- C's share of profit after one year is Rs. 21,600.- We must find the total profit of the business. Concept / Approach:The key concept is that profit is shared in the ratio of capital multiplied by the time period for which it is invested. This forms a proportionality ratio. We compute money-time units for each partner: capital * months. These units give us the ratio in which total profit is divided among A, B and C. Once we know the ratio, we can treat C's share as a fraction of the whole and solve for total profit using a simple proportion. Step-by-Step Solution:Step 1: Let B's capital be 6x; A's capital is 5x.Step 2: C joins after 6 months with capital (2/3) of B's capital, so C's capital = 4x.Step 3: Time invested:- A: 12 months.- B: 12 months.- C: 6 months (joins after 6 months in a 12 month year).Step 4: Money-time units:- A: 5x * 12 = 60x.- B: 6x * 12 = 72x.- C: 4x * 6 = 24x.Step 5: Ratio of profit shares = 60x : 72x : 24x = 5 : 6 : 2 (dividing by 12x).Step 6: Total parts = 5 + 6 + 2 = 13 parts.Step 7: C gets 2 parts out of 13, and this is given as Rs. 21,600.Step 8: So 2 / 13 of total profit = 21,600.Step 9: Total profit = 21,600 * (13 / 2) = 21,600 * 6.5 = 140,400. Verification / Alternative check:Compute 1 part of profit: 140,400 / 13 = 10,800.A's share = 5 * 10,800 = 54,000.B's share = 6 * 10,800 = 64,800.C's share = 2 * 10,800 = 21,600.Sum = 54,000 + 64,800 + 21,600 = 140,400, which matches the calculated total profit, confirming the solution. Why Other Options Are Wrong:- 46800: Too small; it ignores the ratio 5 : 6 : 2 and would make C's share unrealistically large as a fraction of total profit.- 56160: Also too small; it does not produce C's share of 21,600 when using the ratio 5 : 6 : 2.- 70200: Exactly half of the correct answer, corresponding to misinterpreting C's share as 4 out of 13 instead of 2 out of 13. Common Pitfalls:- Forgetting that C joins after 6 months and incorrectly using 12 months instead of 6 for C's time factor.- Using only the capital ratio 5 : 6 : 4 without incorporating the different time periods.- Miscalculating the ratio by neglecting to reduce 60 : 72 : 24 to 5 : 6 : 2.- Doing percentage-based thinking instead of working directly with proportional parts. Final Answer:The total profit of the business at the end of the year is Rs. 1,40,400.

Question 3

A starts a taxi service by investing Rs. 25 lakhs. After 3 months, B joins the business by investing Rs. 40 lakhs, and 4 months after B joins (that is, after a total of 7 months from the start), C also joins by investing Rs. 50 lakhs. One year after…

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Introduction / Context:This is a classic partnership problem with unequal joining times and unequal capital contributions. The partners A, B and C invest different amounts and join the business at different times. Because profit is proportional to both the amount of capital invested and the duration of the investment, we must compute effective contributions in money-time units. The question asks for C's share of the total profit earned over one year from the start of the business. Given Data / Assumptions:- A invests Rs. 25 lakhs from the beginning and remains for 12 months.- B joins after 3 months with Rs. 40 lakhs and remains until the end of the year.- C joins 4 months after B, which is 7 months after A started, with Rs. 50 lakhs and remains until the end of the year.- Total time considered is 12 months from A's start.- Total profit at the end of the year is Rs. 2,73,000.- We are required to find C's share of this profit. Concept / Approach:The key concept is capital-time weighting. Profit share is proportional to capital * time (for example, rupees multiplied by months). For each partner, we compute the product of their capital and the number of months that capital remained invested. The ratio of these products across all partners gives the ratio in which profit is divided. Then, we multiply the total profit by C's fraction of the total ratio to find C's share. Step-by-Step Solution:Step 1: Determine the time each partner's capital is invested.- A: invests for the full 12 months.- B: joins after 3 months, so invests for 12 - 3 = 9 months.- C: joins 4 months after B, i.e., after 7 months from start, so invests for 12 - 7 = 5 months.Step 2: Compute money-time units (capital * months).- A: 25 lakhs * 12 = 300 lakh-months.- B: 40 lakhs * 9 = 360 lakh-months.- C: 50 lakhs * 5 = 250 lakh-months.Step 3: Profit sharing ratio = 300 : 360 : 250.Step 4: Simplify the ratio by dividing by 10: 30 : 36 : 25.Step 5: Total parts = 30 + 36 + 25 = 91.Step 6: C's share fraction = 25 / 91.Step 7: Total profit = Rs. 2,73,000. So C's profit share = (25 / 91) * 2,73,000.Step 8: Compute (25 / 91) * 2,73,000 = 2,73,000 * 25 / 91.Step 9: 2,73,000 / 91 = 3,000. Thus C's share = 3,000 * 25 = Rs. 75,000. Verification / Alternative check:Compute A and B shares to ensure the total adds up.Each part of profit = 2,73,000 / 91 = 3,000.A's share = 30 * 3,000 = Rs. 90,000.B's share = 36 * 3,000 = Rs. 1,08,000.C's share = 25 * 3,000 = Rs. 75,000.Total = 90,000 + 1,08,000 + 75,000 = 2,73,000, which matches the given profit, confirming the answer. Why Other Options Are Wrong:- 100000: Larger than C's actual share; would require C to have a bigger ratio than 25/91.- 125000: Implies C gets nearly half the total profit, inconsistent with the calculated ratio.- 150000: Equal to more than half of the total profit, which is impossible given three partners with substantial contributions. Common Pitfalls:- Ignoring the different joining times and simply using the capital ratio 25 : 40 : 50.- Mixing up months and years, or miscalculating the duration each partner stays in the business.- Not simplifying the ratio correctly and making arithmetic mistakes while finding C's share.- Applying percentage ideas instead of the precise capital-time multiplication method, which is the correct approach for partnership timing questions. Final Answer:C's share of the profit is Rs. 75,000.

Question 4

A, B and C invest in a business in the ratio 4 : 5 : 7. C is a sleeping partner, so his share of profit will be only half of what it would have been if he were a working partner. The firm earns a total profit of Rs. 36,000, out of which 25% is reinv…

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Introduction / Context:This partnership problem involves three partners where one partner, C, is a sleeping partner and therefore receives a reduced share of the profit compared to what his capital ratio alone would entitle him to. The business also reinvests a portion of the profit, meaning that only the remaining part is actually distributed. The task is to calculate B's share of the distributed profit. This type of question strengthens understanding of effective profit-sharing ratios when modifications like sleeping partners and reinvestment occur. Given Data / Assumptions:- Capital investment ratio of A : B : C is 4 : 5 : 7.- C is a sleeping partner.- C's profit share is half of what it would have been if he were a working partner.- Total profit = Rs. 36,000.- 25% of the profit is reinvested in the business.- Thus, 75% of the total profit is distributed among the partners.- We must find B's share in the distributed profit. Concept / Approach:The solution requires adjusting the profit-sharing ratio to account for the reduced share of the sleeping partner. Initially, the ratio 4 : 5 : 7 represents the capital-based shares if everyone were working. For C, we cut his share to half by multiplying his ratio part by 1/2. This yields an effective profit-sharing ratio. We then apply this adjusted ratio to the amount actually distributed (75% of Rs. 36,000) to obtain each partner's share, and particularly B's share. Step-by-Step Solution:Step 1: Base profit-sharing ratio from capital is A : B : C = 4 : 5 : 7.Step 2: Since C is a sleeping partner, his share is half of his normal share.Step 3: C's effective part = 7 * (1/2) = 3.5.Step 4: Effective profit-sharing ratio becomes A : B : C = 4 : 5 : 3.5.Step 5: Sum of these effective parts = 4 + 5 + 3.5 = 12.5.Step 6: Total profit is Rs. 36,000. Only 75% is distributed because 25% is reinvested.Step 7: Distributed profit = 0.75 * 36,000 = Rs. 27,000.Step 8: B's share = (B's effective part / total effective parts) * distributed profit.Step 9: B's share = (5 / 12.5) * 27,000.Step 10: 5 / 12.5 = 0.4, so B's share = 0.4 * 27,000 = Rs. 10,800. Verification / Alternative check:Consider each unit of the effective ratio as representing an equal amount of profit.Total effective parts = 12.5, distributed profit = 27,000.Value per part = 27,000 / 12.5 = 2,160.A's share = 4 * 2,160 = 8,640.B's share = 5 * 2,160 = 10,800.C's share = 3.5 * 2,160 = 7,560.Total = 8,640 + 10,800 + 7,560 = 27,000, which matches the distributed profit, confirming our calculation. Why Other Options Are Wrong:- 7560: This corresponds approximately to C's effective share, not B's share.- 8640: This matches A's share rather than B's share based on the effective ratio.- 9200: This value does not correspond to any correct part multiple from the effective ratio and arises from incorrect percentage or ratio manipulation. Common Pitfalls:- Forgetting to reduce C's share by half and incorrectly using the original ratio 4 : 5 : 7.- Applying the ratio directly to the total profit of Rs. 36,000 instead of to the distributed portion of Rs. 27,000.- Miscalculating 25% and 75%, or using 25% as the distributed amount instead of the reinvested amount.- Treating 3.5 as 3 or 4 when simplifying the ratio, which distorts the final shares. Final Answer:B receives a profit share of Rs. 10,800 from the distributed amount.

Question 5

S, T and U started a business by investing Rs. 4,200, Rs. 6,300 and Rs. 8,400 respectively. S withdrew from the business after 3 months, T withdrew after 6 months, and U remained invested for the full one year. At the end of the year, the total prof…

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Introduction / Context:This question examines profit sharing when partners invest for different lengths of time. Although each person invests a certain capital amount, they do not keep their money in the business for the same duration. Therefore, the share of profit must be based on both capital and time. This approach is crucial in partnership problems and is frequently tested in banking, SSC and other competitive exams. Given Data / Assumptions:- Initial investments are S = Rs. 4,200, T = Rs. 6,300, U = Rs. 8,400.- S withdraws after 3 months, so S is invested for 3 months.- T withdraws after 6 months, so T is invested for 6 months.- U remains invested for the full 12 months (1 year).- Total profit at the end of the year is Rs. 6,000.- We need to find U's share of the profit. Concept / Approach:The central concept is that profit is proportional to capital multiplied by time of investment. These products are often referred to as money-time units, such as rupee-months. We calculate these units for each partner, form a ratio, and then divide the total profit according to that ratio. Finally, U's fraction of the total is applied to Rs. 6,000 to find U's share. Step-by-Step Solution:Step 1: Determine the duration of investment for each partner.- S: 3 months.- T: 6 months.- U: 12 months.Step 2: Compute money-time units (capital * time).- S: 4,200 * 3 = 12,600.- T: 6,300 * 6 = 37,800.- U: 8,400 * 12 = 100,800.Step 3: Form the ratio of profit shares = 12,600 : 37,800 : 100,800.Step 4: Simplify the ratio by dividing all three terms by 4,200.- S: 12,600 / 4,200 = 3.- T: 37,800 / 4,200 = 9.- U: 100,800 / 4,200 = 24.So the ratio is S : T : U = 3 : 9 : 24.Step 5: Sum of ratio parts = 3 + 9 + 24 = 36.Step 6: U's share fraction = 24 / 36 = 2 / 3.Step 7: Total profit = Rs. 6,000. So U's share = (2 / 3) * 6,000 = Rs. 4,000. Verification / Alternative check:Compute each partner's share directly.Each part of the ratio corresponds to 6,000 / 36 = Rs. 166.67 approximately.S's share = 3 * 166.67 ≈ 500.T's share = 9 * 166.67 ≈ 1,500.U's share = 24 * 166.67 ≈ 4,000.The approximate sum is 500 + 1,500 + 4,000 = 6,000, consistent with total profit. Exact fractional calculations give exactly Rs. 4,000 for U. Why Other Options Are Wrong:- 4200: This exceeds the total profit share that U can reasonably get given the ratio and total of 6,000.- 3200: This would correspond to a smaller fraction than 2/3 of the total profit and does not match the money-time ratio.- 3600: This is 60% of the profit, but according to the ratio, U must receive 2/3, that is about 66.67% of the profit. Common Pitfalls:- Ignoring time and using only the capital amounts 4,200 : 6,300 : 8,400 which would be incorrect.- Miscalculating the duration, for example assuming S and T also stay for 12 months.- Arithmetic mistakes when simplifying the ratio or multiplying by the total profit.- Forgetting to express U's share as a fraction of the total ratio before applying it to the profit. Final Answer:U's share of the profit is Rs. 4,000.

Question 6

A profit of Rs. 1,35,200 has to be divided among three partners Aashay, Bhairav and Chetan in the ratio 4 : 3 : 6. How much money, in rupees, does Chetan receive from this profit?

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Introduction / Context:This is a straightforward ratio-based profit-sharing question. The total profit is known and the ratio in which it must be divided among three partners is given. Students must apply the concept of proportional division to determine the exact amount each partner receives. Here, we are specifically asked for Chetan's share. Such questions are common in basic arithmetic and partnership topics and help reinforce the idea of distributing a total amount according to a given ratio. Given Data / Assumptions:- Total profit to be shared = Rs. 1,35,200.- Profit-sharing ratio among Aashay, Bhairav and Chetan is 4 : 3 : 6.- We need to find Chetan's share of the profit.- No time factor or extra conditions such as working or sleeping partners are mentioned. Concept / Approach:The core concept is division of a total quantity in a given ratio. If a total S is to be divided in the ratio p : q : r, then the sum of the parts is p + q + r. Each person's share is the fraction of the total given by their ratio part divided by the total of the parts. Here, we compute the total of the ratio 4 + 3 + 6, then calculate Chetan's fractional share as 6 divided by this sum, and apply it to the profit of Rs. 1,35,200. Step-by-Step Solution:Step 1: Ratio of shares is Aashay : Bhairav : Chetan = 4 : 3 : 6.Step 2: Sum of the ratio parts = 4 + 3 + 6 = 13.Step 3: Chetan's fraction of the total profit is 6 / 13.Step 4: Total profit = Rs. 1,35,200.Step 5: Chetan's share = (6 / 13) * 1,35,200.Step 6: First compute 1,35,200 / 13.- 13 * 10,000 = 1,30,000, leaving 5,200.- 13 * 400 = 5,200.So 1,35,200 / 13 = 10,400.Step 7: Now multiply by 6: Chetan's share = 10,400 * 6 = 62,400.Therefore, Chetan gets Rs. 62,400. Verification / Alternative check:We can verify by calculating all three shares.Each part value = 1,35,200 / 13 = 10,400.Aashay's share = 4 * 10,400 = 41,600.Bhairav's share = 3 * 10,400 = 31,200.Chetan's share = 6 * 10,400 = 62,400.Check the sum: 41,600 + 31,200 + 62,400 = 1,35,200, which matches the total profit. Hence, the distribution is correct. Why Other Options Are Wrong:- 31200: This corresponds to Bhairav's share (3 parts), not Chetan's share.- 41600: This is Aashay's share (4 parts), not Chetan's share.- 93600: This would require Chetan to have 9 parts out of 13, which he does not; it is more than his entitled share based on the ratio. Common Pitfalls:- Adding the ratio numbers incorrectly or forgetting to include one of the partners when summing.- Failing to divide the total profit by the sum of the ratio parts before assigning individual shares.- Mixing up whose ratio part corresponds to which partner while matching the options.- Performing percentage calculations instead of direct ratio-based division, which is more straightforward here. Final Answer:Chetan receives Rs. 62,400 from the profit.

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