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Arithmetic: Partnership — Solved MCQs Solved MCQs

Solved partnership MCQs — 25 questions on profit shares, capital-time ratios, late and leaving partners, withdrawals, charity deductions and investment ratios, with verified answers and explanations. Free online practice for FPSC, PPSC, NTS and all one-paper exams. Covers capital-months and combined ratios.

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This is the Arithmetic: Partnership solved MCQ bank from Advanced FPSC & Other Federal Model Papers (Edition 32): 25 published questions (book pp. 750-752) on profit shares from investment ratios, capital-months with late, leaving and withdrawing partners, subscription differences, combined ratios, charity deductions and capital from a profit claim, each with a worked explanation and a verified answer.

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Arithmetic: Partnership — Solved MCQs

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Subject 1

Mathematics

25 MCQs

Topic Section

Share From Investment Ratio

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Q 1 Mathematics Share From Investment Ratio

A, B and C enter into a partnership. A invests 3 times as much as B invests and B invest two-third of what C invests. At the end of the year, the profit earned is Rs 6600. What is the share of B?

Rs.1200

Rs.1300

Rs.1400

Rs.1500

View answer & explanation Ans: Rs.1200

Correct Answer: Rs.1200

B invests 2 and C 3, so A invests 6; ratio 6:2:3 over 11 parts gives B 2/11 x Rs.6600 = Rs.1200.

Topic Section

Total Rent From One Partner's Share

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Q 2 Mathematics Total Rent From One Partner's Share

Four milkmen rented a pasture. A grazed 24 cows for 3 months; B 10 cows for 5 months; C 35 cows for 4 months and D 21 cows for 3 months. If A's share of rent is Rs.720, find the total rent of the field.

Rs.2850

Rs.3000

3250

Rs.3500

View answer & explanation Ans: 3250

Correct Answer: 3250

Cow-months are 72, 50, 140 and 63, total 325; A's 72 parts are Rs.720, so the total is 325/72 x Rs.720 = Rs.3250.

Topic Section

Partner's Profit Share

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Q 3 Mathematics Partner's Profit Share

Ali and Danish started a business investing Rs.22500 and Rs.35000 respectively. Out of a total profit of Rs.13800, Danish's share is:

Rs.7000

Rs.7800

Rs.8400

Rs.8750

View answer & explanation Ans: Rs.8400

Correct Answer: Rs.8400

Investments are in ratio 9:14 over 23 parts, so Danish gets 14/23 x Rs.13800 = Rs.8400.

Topic Section

Share With Capital And Time

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Q 4 Mathematics Share With Capital And Time

Reema and Shazia are partners in a business. Reema invests Rs.35000 for 8 months and Shazia invests Rs.42000 for 10 months. Out of a profit of Rs.31570, Reema's share is:

Rs.11550

Rs.12628

Rs.12900

Rs.15500

View answer & explanation Ans: Rs.12628

Correct Answer: Rs.12628

Capital-months are 280000 and 420000, ratio 2:3, so Reema gets 2/5 x Rs.31570 = Rs.12628.

Topic Section

Late Partner's Share

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Q 5 Mathematics Late Partner's Share

Kamal started a business investing Rs.9000. After five months, Shahid joined with a capital of Rs.8000. If at the end of the year, they earn a profit of Rs.6970, then what will be share of Shahid in the profit?

Rs.1800

Rs.2380

Rs.2450

Rs.2500

View answer & explanation Ans: Rs.2380

Correct Answer: Rs.2380

Capital-months are 108000 and 56000, ratio 27:14, so Shahid gets 14/41 x Rs.6970 = Rs.2380.

Topic Section

Share By Hours Used

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Q 6 Mathematics Share By Hours Used

A, B, C hired a car for Rs.520 and used it for 7, 8 and 11 hours respectively. Hire charges paid by B are:

Rs.120

Rs.135

Rs.160

Rs.180

View answer & explanation Ans: Rs.160

Correct Answer: Rs.160

Hours are in ratio 7:8:11 over 26 parts, so B pays 8/26 x Rs.520 = Rs.160.

Topic Section

Share Over Two Years With Late Partner

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Q 7 Mathematics Share Over Two Years With Late Partner

A and B started a business in partnership investing Rs.20000 and Rs.15000 respectively. After six months, C joined them with Rs.20000. What will be B's share in the total profit of Rs.25000 earned at the end of 2 years from the starting of the business?

Rs.7500

Rs.7800

Rs.8000

Rs.8200

View answer & explanation Ans: Rs.7500

Correct Answer: Rs.7500

Capital-months over 24 months are 480000, 360000 and 360000, ratio 4:3:3, so B gets 3/10 x Rs.25000 = Rs.7500.

Topic Section

Share When A Partner Leaves Early

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Q 8 Mathematics Share When A Partner Leaves Early

Ali, Kamal and Waleed invested Rs.8000, Rs.4000 and Rs.8000 respectively in a business. Ali left after six months. If after 8 months, there was a gain of Rs.4005, then what will be the share of Kamal?

Rs.750

Rs.890

Rs.925

Rs.990

View answer & explanation Ans: Rs.890

Correct Answer: Rs.890

Capital-months are 48000, 32000 and 64000, ratio 3:2:4, so Kamal gets 2/9 x Rs.4005 = Rs.890.

Topic Section

Excess Of One Partner's Share Over Another

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Q 9 Mathematics Excess Of One Partner's Share Over Another

A and B entered a partnership investing Rs.16000 and Rs.12000 respectively. After 3 months, A withdraw Rs.5000 while B invested Rs.5000 more. After 3 months, C joins the business with a capital Rs.21000. The share of B exceeds that of C, out of a total profit of Rs.26400 after one year by:

Rs.2800

Rs.3000

Rs.3600

Rs.4000

View answer & explanation Ans: Rs.3600

Correct Answer: Rs.3600

Capital-months are A 147000, B 189000 and C 126000 (C for 6 months), so B gets Rs.10800 and C Rs.7200, an excess of Rs.3600.

Topic Section

Shares From Subscription Differences

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Q 10 Mathematics Shares From Subscription Differences

A, B, C subscribe Rs.50000 for a business. A subscribes Rs.4000 more than B and B Rs.5000 more than C. Out of a total profit of Rs.35000, A receives:

Rs.10000

Rs.14700

Rs.15500

Rs.17500

View answer & explanation Ans: Rs.14700

Correct Answer: Rs.14700

Subscriptions are Rs.21000, Rs.17000 and Rs.12000, ratio 21:17:12, so A gets 21/50 x Rs.35000 = Rs.14700.

Topic Section

Share From Capital Relations

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Q 11 Mathematics Share From Capital Relations

Three partners A, B, C start a business. Twice A's capital is equal to thrice B's capital and B's capital is four times C's capital. Out of a total profit of Rs.16500 at the end of year, B's share is:

Rs.5000

Rs.6000

Rs.7000

Rs.8000

View answer & explanation Ans: Rs.6000

Correct Answer: Rs.6000

Capitals are in ratio 6:4:1 over 11 parts, so B gets 4/11 x Rs.16500 = Rs.6000.

Topic Section

Equal Capital Months Shares

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Q 12 Mathematics Equal Capital Months Shares

A, B and C enter into a partnership. A invests some money at the beginning, B invests double the amount after 6 months and C invest thrice the amount after 8 months. If the annual profit be Rs.27000, C's share is:

Rs.20000

Rs.22000

Rs.9000

Rs.7000

View answer & explanation Ans: Rs.9000

Correct Answer: Rs.9000

Capital-months are equal at 12x each (x for 12 months, 2x for 6, 3x for 4), so each partner gets Rs.27000 / 3 = Rs.9000.

Topic Section

Combined Ratio Share

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Q 13 Mathematics Combined Ratio Share

In a business, A and C invested amounts in the ratio 2:1, whereas the ratio between amounts invested by A and B was 3:2. If Rs.157300 was their profit, how much amount did B receive?

Rs.48400

Rs.49500

Rs.50000

Rs.50500

View answer & explanation Ans: Rs.48400

Correct Answer: Rs.48400

Combined capitals are 6:4:3 over 13 parts, so B receives 4/13 x Rs.157300 = Rs.48400.

Topic Section

Share After Partial Withdrawal

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Q 14 Mathematics Share After Partial Withdrawal

A, B and C enter into a partnership and their shares are in the ratio 1/2 : 1/3 : 1/4. After 2 months, A withdraws half of his capital and after 10 months, a profit of Rs.378 is divided among them. What is B's share?

Rs.100

Rs.114

Rs.144

Rs.160

View answer & explanation Ans: Rs.144

Correct Answer: Rs.144

Capitals 6:4:3 over 12 months give capital-months A 6x2 + 3x10 = 42, B 48, C 36, total 126, so B gets 48/126 x Rs.378 = Rs.144.

Topic Section

Share After A Partner Increases Capital

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Q 15 Mathematics Share After A Partner Increases Capital

A, B and C enter into a partnership in the ratio 7/2 : 4/3 : 6/5. After 4 months, A increases his share by 50%. If the total profit at the end of one year be Rs.21600, then B's share in the profit is:

Rs.2000

Rs.4000

Rs.5000

Rs.7000

View answer & explanation Ans: Rs.4000

Correct Answer: Rs.4000

Capitals 105:40:36 give capital-months A 105x4 + 157.5x8 = 1680, B 480, C 432, total 2592, so B gets 480/2592 x Rs.21600 = Rs.4000.

Topic Section

Share After Both Partners Withdraw

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Q 16 Mathematics Share After Both Partners Withdraw

A and B entered into a partnership with capitals in the ratio 4:5. After 3 months, A withdraw 1/4 of his capital and B withdraw 1/5 of his capital. The gain at the end of 10 months was Rs.760. A's share in this profit is:

Rs.300

Rs.330

Rs.360

Rs.400

View answer & explanation Ans: Rs.330

Correct Answer: Rs.330

Capital-months are A 4x3 + 3x7 = 33 and B 5x3 + 4x7 = 43, total 76, so A gets 33/76 x Rs.760 = Rs.330.

Topic Section

Share From Capital And Time Fractions

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Q 17 Mathematics Share From Capital And Time Fractions

In a partnership, A invests 1/6 of the capital for 1/6 of the time, B invests 1/3 of the capital for 1/3 of the time and C, the rest of the capital for the whole time. Out of a profit of Rs.4600, B's share is:

Rs.500

Rs.600

Rs.800

Rs.900

View answer & explanation Ans: Rs.800

Correct Answer: Rs.800

Capital-time products are 1/36, 4/36 and 18/36, ratio 1:4:18, so B gets 4/23 x Rs.4600 = Rs.800.

Topic Section

Capital From Profit Ratio

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Q 18 Mathematics Capital From Profit Ratio

X and Y invested in a business. They earned some profit with which they divided in the ratio of 2:3. If X invested Rs.40000, the amount invested by Y is:

Rs.30000

Rs.40000

Rs.60000

Rs.70000

View answer & explanation Ans: Rs.60000

Correct Answer: Rs.60000

Capital follows the profit ratio 2:3 for equal time, so Y invested 3/2 x Rs.40000 = Rs.60000.

Topic Section

Capital From Profit Shares

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Q 19 Mathematics Capital From Profit Shares

A, B and C enter into a partnership with a capital in which A's contribution is Rs.10000. If out of a total profit of Rs.1000, A gets Rs.500 and B gets Rs.300, then C's capital is:

Rs.3000

Rs.4000

Rs.5000

Rs.6000

View answer & explanation Ans: Rs.4000

Correct Answer: Rs.4000

C's profit share is Rs.1000 - Rs.500 - Rs.300 = Rs.200, so capitals are in ratio 5:3:2 and C's capital is 2/5 x Rs.10000 = Rs.4000; the printed key (c) Rs.5000 is overridden.

Topic Section

Total Profit From One Partner's Share

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Q 20 Mathematics Total Profit From One Partner's Share

A, B and C started a shop by investing Rs.27000, Rs.72000 and Rs.81000 respectively. At the end of the year, the profits were distributed among them. If C's share of profit be Rs.36000, then the total profit was:

Rs.50000

Rs.60000

Rs.80000

Rs.90000

View answer & explanation Ans: Rs.80000

Correct Answer: Rs.80000

Investments are in ratio 3:8:9 over 20 parts, so C's 9 parts are Rs.36000 and the total is 20/9 x Rs.36000 = Rs.80000.

Topic Section

Total Profit From Capital Time Ratio

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Q 21 Mathematics Total Profit From Capital Time Ratio

A and B started a business jointly. 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 received Rs.4000 as profit, then their total profit is:

Rs.20000

Rs.22000

Rs.28000

Rs.29000

View answer & explanation Ans: Rs.28000

Correct Answer: Rs.28000

Capital-time ratio is 6:1 over 7 parts, so B's Rs.4000 is 1 part and the total is 7 x Rs.4000 = Rs.28000.

Topic Section

Partner's Capital From Profit Ratio

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Q 22 Mathematics Partner's Capital From Profit Ratio

A starts business with Rs.3500 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2:3. What is B's contribution in the capital?

Rs.5000

Rs.7000

Rs.8000

Rs.9000

View answer & explanation Ans: Rs.9000

Correct Answer: Rs.9000

A's capital-months are Rs.3500 x 12 = 42000, so B's are 3/2 x 42000 = 63000 over 7 months, giving a capital of Rs.9000.

Topic Section

Capital From Profit Claim And Time

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Q 23 Mathematics Capital From Profit Claim And Time

A and B started a business jointly. A invests Rs.16000 for 8 months and B remains in the business for 4 months. Out of total profit, B claims 2/7 of the profit. How much money was contributed by B.

Rs.10000

Rs.10500

Rs.12800

Rs.14500

View answer & explanation Ans: Rs.12800

Correct Answer: Rs.12800

A's capital-months are 128000 for 5/7 of the profit, so B's are 2/5 x 128000 = 51200 over 4 months, giving a capital of Rs.12800.

Topic Section

Total Profit After Charity Deduction

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Q 24 Mathematics Total Profit After Charity Deduction

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:

Rs.1500

Rs.1400

Rs.1350

Rs.1300

View answer & explanation Ans: Rs.1500

Correct Answer: Rs.1500

After 5% charity, A gets 3/5 of 95% = 57% of the total, so the total is Rs.855 / 0.57 = Rs.1500.

Topic Section

Time From Capital And Profit Shares

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Q 25 Mathematics Time From Capital And Profit Shares

A and B are partners in a business. A contributes 1/4 of the capital for 15 months and B receive 2/3 of the profit. For how long B's money was used?

2 months

10 months

one year

2 years

View answer & explanation Ans: 10 months

Correct Answer: 10 months

A contributes 1/4 of the capital for 15 months (15/4) and B 3/4 for t months (3t/4); profit ratio 1:2 gives 5:t = 1:2, so t = 10 months.

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FPSC Past Papers Arithmetic Partnership — All Years All Past Papers Mathematics MCQs

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How many questions are in the Arithmetic: Partnership MCQ bank? +

25 questions, all printed in the book and all published. No item is dropped: every question has a unique correct option once the book's numbers are worked through.

What does the Arithmetic: Partnership bank cover? +

Profit shares from investment ratios, capital-months for partners who join late, leave early, withdraw or increase capital, subscription differences, combined ratios, totals from one partner's share, charity deductions, and finding a partner's capital or time from a profit claim.

Are the answers in the Partnership bank verified? +

Yes. Every published answer was solved from scratch and checked against the book's printed Answer Key (p. 752); the key agrees on 24 of the 25 items, and the one disagreement (a partner's capital of Rs.4000, keyed as Rs.5000) is corrected to the verified answer, with the working shown in the explanation.

Which exams does the Partnership bank help with? +

It is drawn from an FPSC model-paper book, but partnership and profit-sharing problems appear in the same form in PPSC, NTS, PTS, CSS MPT and all Pakistan one-paper exams, so it serves aspirants of every body.

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Arithmetic: Partnership — Solved MCQs Solved MCQs

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Mathematics

Share From Investment Ratio

A, B and C enter into a partnership. A invests 3 times as much as B invests and B invest two-third of what C invests. At the end of the year, the profit earned is Rs 6600. What is the share of B?

Total Rent From One Partner's Share

Four milkmen rented a pasture. A grazed 24 cows for 3 months; B 10 cows for 5 months; C 35 cows for 4 months and D 21 cows for 3 months. If A's share of rent is Rs.720, find the total rent of the field.

Partner's Profit Share

Ali and Danish started a business investing Rs.22500 and Rs.35000 respectively. Out of a total profit of Rs.13800, Danish's share is:

Share With Capital And Time

Reema and Shazia are partners in a business. Reema invests Rs.35000 for 8 months and Shazia invests Rs.42000 for 10 months. Out of a profit of Rs.31570, Reema's share is:

Late Partner's Share

Kamal started a business investing Rs.9000. After five months, Shahid joined with a capital of Rs.8000. If at the end of the year, they earn a profit of Rs.6970, then what will be share of Shahid in the profit?

Share By Hours Used

A, B, C hired a car for Rs.520 and used it for 7, 8 and 11 hours respectively. Hire charges paid by B are:

Share Over Two Years With Late Partner

A and B started a business in partnership investing Rs.20000 and Rs.15000 respectively. After six months, C joined them with Rs.20000. What will be B's share in the total profit of Rs.25000 earned at the end of 2 years from the starting of the business?

Share When A Partner Leaves Early

Ali, Kamal and Waleed invested Rs.8000, Rs.4000 and Rs.8000 respectively in a business. Ali left after six months. If after 8 months, there was a gain of Rs.4005, then what will be the share of Kamal?

Excess Of One Partner's Share Over Another

A and B entered a partnership investing Rs.16000 and Rs.12000 respectively. After 3 months, A withdraw Rs.5000 while B invested Rs.5000 more. After 3 months, C joins the business with a capital Rs.21000. The share of B exceeds that of C, out of a total profit of Rs.26400 after one year by:

Shares From Subscription Differences

A, B, C subscribe Rs.50000 for a business. A subscribes Rs.4000 more than B and B Rs.5000 more than C. Out of a total profit of Rs.35000, A receives:

Share From Capital Relations

Three partners A, B, C start a business. Twice A's capital is equal to thrice B's capital and B's capital is four times C's capital. Out of a total profit of Rs.16500 at the end of year, B's share is:

Equal Capital Months Shares

A, B and C enter into a partnership. A invests some money at the beginning, B invests double the amount after 6 months and C invest thrice the amount after 8 months. If the annual profit be Rs.27000, C's share is:

Combined Ratio Share

In a business, A and C invested amounts in the ratio 2:1, whereas the ratio between amounts invested by A and B was 3:2. If Rs.157300 was their profit, how much amount did B receive?

Share After Partial Withdrawal

A, B and C enter into a partnership and their shares are in the ratio 1/2 : 1/3 : 1/4. After 2 months, A withdraws half of his capital and after 10 months, a profit of Rs.378 is divided among them. What is B's share?

Share After A Partner Increases Capital

A, B and C enter into a partnership in the ratio 7/2 : 4/3 : 6/5. After 4 months, A increases his share by 50%. If the total profit at the end of one year be Rs.21600, then B's share in the profit is:

Share After Both Partners Withdraw

A and B entered into a partnership with capitals in the ratio 4:5. After 3 months, A withdraw 1/4 of his capital and B withdraw 1/5 of his capital. The gain at the end of 10 months was Rs.760. A's share in this profit is:

Share From Capital And Time Fractions

In a partnership, A invests 1/6 of the capital for 1/6 of the time, B invests 1/3 of the capital for 1/3 of the time and C, the rest of the capital for the whole time. Out of a profit of Rs.4600, B's share is:

Capital From Profit Ratio

X and Y invested in a business. They earned some profit with which they divided in the ratio of 2:3. If X invested Rs.40000, the amount invested by Y is:

Capital From Profit Shares

A, B and C enter into a partnership with a capital in which A's contribution is Rs.10000. If out of a total profit of Rs.1000, A gets Rs.500 and B gets Rs.300, then C's capital is:

Total Profit From One Partner's Share

A, B and C started a shop by investing Rs.27000, Rs.72000 and Rs.81000 respectively. At the end of the year, the profits were distributed among them. If C's share of profit be Rs.36000, then the total profit was:

Total Profit From Capital Time Ratio

A and B started a business jointly. 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 received Rs.4000 as profit, then their total profit is:

Partner's Capital From Profit Ratio

A starts business with Rs.3500 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2:3. What is B's contribution in the capital?

Capital From Profit Claim And Time

A and B started a business jointly. A invests Rs.16000 for 8 months and B remains in the business for 4 months. Out of total profit, B claims 2/7 of the profit. How much money was contributed by B.

Total Profit After Charity Deduction

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:

Time From Capital And Profit Shares

A and B are partners in a business. A contributes 1/4 of the capital for 15 months and B receive 2/3 of the profit. For how long B's money was used?

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