Sharing profit by capital and time.
45 solved questions · 15 easy · 20 medium · 10 hard
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A and B start a business with ₹12,000 and ₹18,000 respectively and run it for one year. The profit is ₹15,000. What is A's share?
Answer: C. ₹6,000
Solution
Time is equal, so ratio = capital ratio = 12000 : 18000 = 2:3 A's share = 2/5 of 15,000 = ₹6,000 Answer: ₹6,000
Shortcut: Equal time: divide the profit in the capital ratio 2:3, so A gets 2/5.
A, B and C invest ₹5,000, ₹7,000 and ₹8,000 for the same period. Out of a profit of ₹30,000, how much does C get?
Answer: A. ₹12,000
Solution
Ratio = 5 : 7 : 8 (total 20 parts) C's share = 8/20 of 30,000 = ₹12,000 Answer: ₹12,000
A, B and C invest in the ratio 2 : 3 : 5 for the same time. If the total profit is ₹60,000, find B's share.
Answer: D. ₹18,000
Solution
Total parts = 2+3+5 = 10 B's share = 3/10 of 60,000 = ₹18,000 Answer: ₹18,000
A and B invest ₹8,000 and ₹6,000 for the same period. If A's share of the profit is ₹12,000, what is the total profit?
Answer: B. ₹21,000
Solution
Ratio = 8000 : 6000 = 4 : 3 A's 4 parts = ₹12,000, so 1 part = ₹3,000 Total = 7 parts = 7 x 3,000 = ₹21,000 Answer: ₹21,000
A and B invest the same amount, A for 12 months and B for 8 months. The profit is ₹25,000. What does B get?
Answer: C. ₹10,000
Solution
Capital is equal, so ratio = time ratio = 12 : 8 = 3 : 2 B's share = 2/5 of 25,000 = ₹10,000 Answer: ₹10,000
A invests ₹6,000 for 8 months and B invests ₹4,000 for 12 months. They earn ₹18,000 in all. What is A's share?
Answer: A. ₹9,000
Solution
A: 6000 x 8 = 48,000 B: 4000 x 12 = 48,000 Ratio = 1 : 1, so each gets half of 18,000 = ₹9,000 Answer: ₹9,000
Shortcut: Always multiply capital by time; comparing capitals alone (3:2) gives the wrong ₹10,800.
A and B invest for the same time and share profit in the ratio 3 : 2. If A invested ₹15,000, how much did B invest?
Answer: D. ₹10,000
Solution
Profit ratio = capital ratio = 3 : 2 A's 3 parts = 15,000, so 1 part = 5,000 B = 2 x 5,000 = ₹10,000 Answer: ₹10,000
A and B invest ₹20,000 and ₹30,000 for the same period and suffer a loss of ₹10,000. How much of the loss does A bear?
Answer: B. ₹4,000
Solution
Loss is shared in the capital ratio 2 : 3 A's share = 2/5 of 10,000 = ₹4,000 Answer: ₹4,000
A, B and C invest ₹4,000, ₹6,000 and ₹10,000 for the same time. The profit is ₹40,000. By how much does C's share exceed A's?
Answer: C. ₹12,000
Solution
Ratio = 2 : 3 : 5 (10 parts), 1 part = ₹4,000 A = 8,000, C = 20,000 Difference = ₹12,000 Answer: ₹12,000
A starts a business with ₹25,000. B joins after 4 months with ₹30,000. At the end of the year the profit is ₹18,000. What is B's share?
Answer: A. ₹8,000
Solution
A: 25000 x 12 = 3,00,000 B: 30000 x 8 = 2,40,000 Ratio = 300 : 240 = 5 : 4 B's share = 4/9 of 18,000 = ₹8,000 Answer: ₹8,000
A and B invest in the ratio 3 : 5. A's money stays for 8 months and B's for 6 months. If the profit is ₹27,000, what is A's share?
Answer: D. ₹12,000
Solution
A : B = 3x8 : 5x6 = 24 : 30 = 4 : 5 A's share = 4/9 of 27,000 = ₹12,000 Answer: ₹12,000
A and B invest in the ratio 5 : 3 for the same time. A gets ₹6,000 more than B out of the profit. What is the total profit?
Answer: B. ₹24,000
Solution
Ratio 5 : 3, difference = 2 parts = ₹6,000 1 part = ₹3,000 Total = 8 parts = ₹24,000 Answer: ₹24,000
A invests ₹30,000 for the full year and B joins after 3 months. They share the profit equally. How much did B invest?
Answer: C. ₹40,000
Solution
Equal profit means equal (capital x time) A: 30,000 x 12 = 3,60,000 B: x for 9 months, so 9x = 3,60,000 x = ₹40,000 Answer: ₹40,000
A invests ₹10,000 for 12 months, B invests ₹15,000 for 8 months and C invests ₹12,000 for 10 months. The profit is ₹27,000. What does C get?
Answer: A. ₹9,000
Solution
A: 10,000 x 12 = 1,20,000 B: 15,000 x 8 = 1,20,000 C: 12,000 x 10 = 1,20,000 All equal, so each gets 27,000 / 3 = ₹9,000 Answer: ₹9,000
A and B invest ₹7,000 and ₹14,000 for the same period. If the profit is ₹12,000, what is B's share?
Answer: D. ₹8,000
Solution
Ratio = 7000 : 14000 = 1 : 2 B's share = 2/3 of 12,000 = ₹8,000 Answer: ₹8,000
A and B invest ₹30,000 and ₹20,000. A manages the business and gets 10% of the profit as commission; the rest is divided in proportion to capital. If the profit is ₹50,000, find A's total.
Answer: B. ₹32,000
Solution
Commission = 10% of 50,000 = ₹5,000 Remaining = ₹45,000, divided 3 : 2 A's share = 27,000 A's total = 27,000 + 5,000 = ₹32,000 Answer: ₹32,000
A (capital ₹20,000) and B (capital ₹40,000) are partners. A, the working partner, gets 12% of the profit first and the rest is shared by capital. If the profit is ₹30,000, what does B get?
Answer: C. ₹17,600
Solution
A's commission = 12% of 30,000 = ₹3,600 Remaining = ₹26,400, divided 1 : 2 B's share = 2/3 of 26,400 = ₹17,600 Answer: ₹17,600
A starts a business with ₹30,000. After 6 months B joins with ₹40,000. At the end of the year the profit is ₹45,000. What is A's share?
Answer: A. ₹27,000
Solution
A: 30000 x 12 = 3,60,000 B: 40000 x 6 = 2,40,000 Ratio = 3 : 2 A's share = 3/5 of 45,000 = ₹27,000 Answer: ₹27,000
A has ₹40,000 and B has ₹30,000 in a business. After 6 months A withdraws half of his capital. At the end of the year the profit is ₹24,000. What is A's share?
Answer: D. ₹12,000
Solution
A: 40000 x 6 + 20000 x 6 = 2,40,000 + 1,20,000 = 3,60,000 B: 30000 x 12 = 3,60,000 Ratio = 1 : 1 A's share = 24,000 / 2 = ₹12,000 Answer: ₹12,000
A invests 3 times as much as B, and B invests two-thirds of what C invests. The time is the same. If the total profit is ₹22,000, what is A's share?
Answer: B. ₹12,000
Solution
Let C = 3x. Then B = 2x and A = 6x Ratio A : B : C = 6 : 2 : 3 (total 11) A's share = 6/11 of 22,000 = ₹12,000 Answer: ₹12,000
A invests ₹12,000 for 12 months and B invests ₹8,000 for some months. They share profit in the ratio 2 : 1. For how many months was B's money invested?
Answer: C. 9 months
Solution
A: 12,000 x 12 = 1,44,000 B: 8,000 x t 1,44,000 : 8,000t = 2 : 1 8,000t = 72,000 t = 9 months Answer: 9 months
A invests ₹20,000 for 12 months, B invests ₹30,000 for 8 months and C invests ₹40,000 for 9 months. The profit is ₹35,000. Find C's share.
Answer: A. ₹15,000
Solution
A: 2,40,000; B: 2,40,000; C: 3,60,000 Ratio = 2 : 2 : 3 (total 7) C's share = 3/7 of 35,000 = ₹15,000 Answer: ₹15,000
Out of a total profit of ₹90,000, 10% is first given to charity. The remaining is shared by A, B and C in the ratio 4 : 5 : 6. How much does B get?
Answer: D. ₹27,000
Solution
After charity: 90,000 - 9,000 = ₹81,000 B's share = 5/15 of 81,000 = ₹27,000 Answer: ₹27,000
A starts a business with ₹45,000. B joins after 3 months with ₹60,000 and C joins after 6 months with ₹90,000. At the end of the year the profit is ₹90,000. What is C's share?
Answer: B. ₹30,000
Solution
A: 45,000 x 12 = 5,40,000 B: 60,000 x 9 = 5,40,000 C: 90,000 x 6 = 5,40,000 All equal, so each gets 90,000 / 3 = ₹30,000 Answer: ₹30,000
A and B invest in the ratio 5 : 6. A's money is used for 8 months and B's for 5 months. If the total profit is ₹28,000, what is A's share?
Answer: C. ₹16,000
Solution
A : B = 5x8 : 6x5 = 40 : 30 = 4 : 3 A's share = 4/7 of 28,000 = ₹16,000 Answer: ₹16,000
A, B and C together invest ₹95,000 for one year. A invests ₹10,000 more than B, and B invests ₹5,000 more than C. The profit is ₹38,000. What is A's share?
Answer: A. ₹16,000
Solution
Let C = x, B = x + 5,000, A = x + 15,000 3x + 20,000 = 95,000, so x = 25,000 Capitals: A = 40,000, B = 30,000, C = 25,000; ratio 8 : 6 : 5 (19 parts) 1 part = 38,000 / 19 = ₹2,000 A = 8 x 2,000 = ₹16,000 Answer: ₹16,000
A invests ₹16,000 for 8 months and B invests some money for 12 months. Out of a profit of ₹25,000, A gets ₹10,000. How much did B invest?
Answer: D. ₹16,000
Solution
A gets 10,000, so B gets 15,000: ratio 2 : 3 A: 16,000 x 8 = 1,28,000 B's capital x time = 1,28,000 x 3/2 = 1,92,000 B's capital = 1,92,000 / 12 = ₹16,000 Answer: ₹16,000
A invests ₹8,000 for the whole year. B invests ₹6,000 for the first 4 months and then adds ₹2,000 more for the remaining 8 months. The year's profit is ₹23,000. How much does B get?
Answer: B. ₹11,000
Solution
A: 8,000 x 12 = 96,000 B: 6,000 x 4 + 8,000 x 8 = 24,000 + 64,000 = 88,000 Ratio = 96 : 88 = 12 : 11 B's share = 11/23 of 23,000 = ₹11,000 Answer: ₹11,000
A, B and C invest ₹30,000 for 8 months, ₹20,000 for 12 months and ₹25,000 for 6 months. They make a loss of ₹42,000. How much loss does C bear?
Answer: C. ₹10,000
Solution
A: 2,40,000; B: 2,40,000; C: 1,50,000 Ratio = 8 : 8 : 5 (21 parts) C's loss = 5/21 of 42,000 = ₹10,000 Answer: ₹10,000
A and B start with ₹24,000 and ₹36,000. After 6 months C joins with some capital. At the end of the year C's share is 1/4 of the total profit. How much did C invest?
Answer: A. ₹40,000
Solution
A: 24,000 x 12 = 2,88,000 B: 36,000 x 12 = 4,32,000 A + B = 7,20,000 and they share 3/4 of the profit C's share is 1/3 of (A + B) = 2,40,000 C invested for 6 months: capital = 2,40,000 / 6 = ₹40,000 Answer: ₹40,000
Three partners invest in the ratio 1 : 2 : 3 and their investment periods are in the ratio 3 : 2 : 1. If the total profit is ₹50,000, what does the second partner get?
Answer: D. ₹20,000
Solution
Ratio = 1x3 : 2x2 : 3x1 = 3 : 4 : 3 (10 parts) Second partner = 4/10 of 50,000 = ₹20,000 Answer: ₹20,000
Three farmers graze cattle on a pasture: A keeps 6 cows for 8 months, B keeps 8 cows for 6 months and C keeps 9 cows for 8 months. The total rent is ₹2,520. How much does C pay?
Answer: B. ₹1,080
Solution
Cow-months: A = 48, B = 48, C = 72 (total 168) Rent per cow-month = 2,520 / 168 = ₹15 C pays 72 x 15 = ₹1,080 Answer: ₹1,080
Three partners share profit in the ratio 4 : 5 : 6 for equal time. The second partner's share exceeds the first partner's by ₹1,200. What is the total profit?
Answer: C. ₹18,000
Solution
Ratio 4 : 5 : 6 (15 parts) Difference between 2nd and 1st = 5 - 4 = 1 part = ₹1,200 Total = 15 x 1,200 = ₹18,000 Answer: ₹18,000
A, B and C invest in the ratio 2 : 3 : 5. C withdraws his whole capital after 6 months while the others stay for the full year. If the profit is ₹45,000, what does C get?
Answer: A. ₹15,000
Solution
Ratio = 2x12 : 3x12 : 5x6 = 24 : 36 : 30 = 4 : 6 : 5 C's share = 5/15 of 45,000 = ₹15,000 Answer: ₹15,000
A (capital ₹40,000) and B (capital ₹60,000) run a firm. A, as the working partner, gets a salary of ₹1,500 per month. The year's profit (before salary) is ₹1,00,000. How much does A receive in all?
Answer: D. ₹50,800
Solution
Salary = 1,500 x 12 = ₹18,000 Remaining profit = 1,00,000 - 18,000 = ₹82,000 Shared 2 : 3, A gets 2/5 of 82,000 = ₹32,800 A's total = 32,800 + 18,000 = ₹50,800 Answer: ₹50,800
A starts with ₹36,000. B joins after 3 months with ₹48,000 and C joins after 5 months with ₹60,000. At the end of the year the total profit is ₹1,07,000. What is C's share?
Answer: B. ₹35,000
Solution
A: 36,000 x 12 = 4,32,000 B: 48,000 x 9 = 4,32,000 C: 60,000 x 7 = 4,20,000 Ratio = 432 : 432 : 420 = 36 : 36 : 35 (107 parts) 1 part = ₹1,000, C = ₹35,000 Answer: ₹35,000
A invests ₹80,000 for the whole year. B invests ₹60,000 but joins late. At the end of the year B's share is exactly one-third of the total profit. After how many months did B join?
Answer: C. 4 months
Solution
B's share is 1/3, so A : B = 2 : 1 A: 80,000 x 12 = 9,60,000, so B = 4,80,000 B's months = 4,80,000 / 60,000 = 8 B joined after 12 - 8 = 4 months Answer: 4 months
A has ₹60,000 and B has ₹40,000 in a business. After 5 months A withdraws ₹20,000 and B adds ₹20,000. At the end of the year the profit is ₹60,000. What is A's share?
Answer: A. ₹29,000
Solution
A: 60,000 x 5 + 40,000 x 7 = 3,00,000 + 2,80,000 = 5,80,000 B: 40,000 x 5 + 60,000 x 7 = 2,00,000 + 4,20,000 = 6,20,000 Ratio = 29 : 31 (60 parts), 1 part = ₹1,000 A's share = ₹29,000 Answer: ₹29,000
A (capital ₹50,000) and B (capital ₹70,000) are partners for a year. A also manages the firm and gets 10% of the total profit of ₹1,20,000 as commission before the rest is divided by capital. By how much does B's total exceed A's?
Answer: D. ₹6,000
Solution
Commission = ₹12,000, remaining = ₹1,08,000 Capital ratio 5 : 7: A gets 45,000, B gets 63,000 A's total = 45,000 + 12,000 = 57,000 B's total = 63,000 Difference = ₹6,000 Answer: ₹6,000
A, B and C invest ₹20,000, ₹30,000 and ₹50,000. A manages the business and gets 5% of the total profit as commission; the rest is divided by capital. If C's share exceeds A's total by ₹14,100, find the total profit.
Answer: B. ₹60,000
Solution
Let the profit be P. Commission = 0.05P; remaining = 0.95P shared 2 : 3 : 5 A's total = 0.05P + 0.19P = 0.24P C's share = 0.475P Difference = 0.235P = 14,100 P = 14,100 / 0.235 = ₹60,000 Answer: ₹60,000
A and B start with ₹9,000 and ₹6,000. After 4 months A withdraws one-third of his capital and B increases his capital by 50%. At the end of the year the profit is ₹45,000. What is A's share?
Answer: C. ₹21,000
Solution
A: 9,000 x 4 + 6,000 x 8 = 36,000 + 48,000 = 84,000 B: 6,000 x 4 + 9,000 x 8 = 24,000 + 72,000 = 96,000 Ratio = 84 : 96 = 7 : 8 A's share = 7/15 of 45,000 = ₹21,000 Answer: ₹21,000
A invests ₹10,000 for 12 months, B invests ₹20,000 for some months and C invests ₹20,000 for 6 months. B gets 40% of the total profit. For how many months was B's money invested?
Answer: A. 8 months
Solution
A: 10,000 x 12 = 1,20,000; C: 20,000 x 6 = 1,20,000 A + C get 60% of profit, so 1,20,000 + 1,20,000 = 2,40,000 stands for 60% B (40%) = 2,40,000 x 40/60 = 1,60,000 B's months = 1,60,000 / 20,000 = 8 Answer: 8 months
A starts with ₹70,000. B joins after 3 months with ₹60,000 and C joins after another 3 months with ₹1,20,000. The profit at the end of the year is ₹3,50,000. What is C's share?
Answer: D. ₹1,20,000
Solution
A: 70,000 x 12 = 8,40,000 B: 60,000 x 9 = 5,40,000 C: 1,20,000 x 6 = 7,20,000 Ratio = 14 : 9 : 12 (35 parts) 1 part = ₹10,000, C's share = ₹1,20,000 Answer: ₹1,20,000
A has ₹70,000 and B has ₹50,000 in a business. After 8 months B withdraws one-fifth of his capital. The profit for the year is ₹75,000. What is B's share?
Answer: B. ₹30,000
Solution
A: 70,000 x 12 = 8,40,000 B: 50,000 x 8 + 40,000 x 4 = 4,00,000 + 1,60,000 = 5,60,000 Ratio = 3 : 2 B's share = 2/5 of 75,000 = ₹30,000 Answer: ₹30,000
A, B and C invest in the ratio 1/2 : 1/3 : 1/6 and their times of investment are in the ratio 2 : 3 : 4. If the profit is ₹40,000, what does A get?
Answer: C. ₹15,000
Solution
Capital ratio 1/2 : 1/3 : 1/6 = 3 : 2 : 1 Profit ratio = 3x2 : 2x3 : 1x4 = 6 : 6 : 4 = 3 : 3 : 2 (8 parts) A's share = 3/8 of 40,000 = ₹15,000 Answer: ₹15,000
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