Partnership Business
Class 10th Mathematics West Bengal Board Solution
- I and my friend Mala together have started a business with capitals of ₹15000 and…
- Priyam, Supriya and Bulu have opened a small shop of grocery shop with capitals of…
- Shobha and Masud together bought a car for ₹250000 and sold it for ₹262,500. If Sobha…
- Three friends started a partnership business by investing ₹5000, ₹6000 and ₹7000…
- Dipu, Rabeya and Megha have started a small business by investing the capitals of…
- Three friends have started a business by investing ₹8000, ₹10000 and ₹12000…
- Three friends took loans of ₹6000, ₹8000 and ₹5000 respectively from a co-operative…
- Three friends invested ₹12000, ₹15000 and ₹110000 respectively to purchase a bus. The…
- Pradipbabu and Aminabibi started a business by investing ₹24000 and ₹30000 respectively…
- Niyamat chacha and Karabi didi have started a partnership business together by…
- Srikant and Soiffuddin invested ₹240000 and ₹30,0000 respectively at the beginning of…
- Arun and Ajoy started a business jointly by investing ₹24000 and ₹30000 respectively…
- Three clay modellers from Kumartuli collectively took a loan of ₹100000 from a…
- Two friends invested ₹40000 and ₹50000 respectively to start a business. They made a…
- Puja, Uttam and Meher started a partnership business with capitals of ₹5000, ₹7000 and…
- Q16A1 The capitals of three friends in a partnership business are ₹200, ₹150 and ₹250…
- Q16A2 Suvendu and Noused started a business with capitals of ₹1500 and ₹1000. After a year…
- Q16A3 Fatima, Shreya and Smita started a business by investing total ₹6000. After a year…
- Q16A4 Amal and Bimal started a business. Amal invested ₹500 for 9 months and Bimal…
- Q16A5 Pallabi invested ₹500 for 9 months and Rajiya invested ₹600 for 5 months in a…
- Let us write whether the following statements are true or false: (i) At least 3…
- Let us fill in the blanks: (i) Partnership business is _______types. (ii) Without any…
- In partnership business the ratio of capitals of Samir, Idrish and Antorny are as 1/6…
- If a partnership business the ratio of capitals of Pritha and Rabeya is 2:3 and the…
- The total profit is ₹1500 in a partnership business of two persons. If the capital of…
- The ratio of capitals of three persons is 3:8:5, and the profit of 1st person is ₹60…
- Jayanta, Ajit and Kunal started partnership business investing ₹15000. At the end of…
Let Us See By Calculating 14
Question 1.I and my friend Mala together have started a business with capitals of ₹15000 and ₹25000 respectively. If we make a profit of ₹16,800 in a year, let us see that profit share shall we each get?
Answer:
I invested = ₹15000 for a year
Mala invested = ₹25000 for a year
My total investment = ₹15000 × 12
Mala’s total investment = ₹25000 × 12
Ratio of partnership = 15000×12 : 25000×12
= 15 : 25
= 3 : 5
Total profit made = ₹16,800
= 3×2100
= ₹6300
= 5×2100
= ₹10500
Question 2.
Priyam, Supriya and Bulu have opened a small shop of grocery shop with capitals of ₹15000, ₹10000 and ₹25000 respectively. But after a year there was a loss of ₹3000. Let us write by calculating what each must pay to make up the loss.
Answer:
Priyam invested = ₹15000 for a year
Supriya invested = ₹10000 for a year
Bulu invested = ₹25000 for a year
Bulu’s total investment = ₹25000 × 12
Supriya’s total investment = ₹10000 × 12
Priyam’s total investment = ₹15000 × 12
Ratio of partnership = 15000×12 : 10000×12 : 25000 × 12
= 3 : 2 : 5
Loss incurred = ₹3000
= ₹900
= ₹600
= ₹1500
Question 3.
Shobha and Masud together bought a car for ₹250000 and sold it for ₹262,500. If Sobha paid 
times more than Masud, let us write by calculating their shares of profit.
Answer:
Let Masud pay x.
Bought a car for = ₹250000
Sold a car for = ₹262,500
∴ Profit = ₹262,500 - ₹250000
= ₹12500
= 1.5 : 1
= ₹ 7500
= ₹ 5000
Question 4.
Three friends started a partnership business by investing ₹5000, ₹6000 and ₹7000 respectively. After running the business for one year, they found that there is a loss of ₹1800. They decided to pay to make up that loss to undistribute their capitals. Let us write by calculating the amount they have to pay.
Answer:
Given, 3 friends, say A, B and C, started a partnership business by investing ₹5000, ₹6000 and ₹7000 respectively for a year.
Ratio of partnership = 5000×12 : 6000×12 : 7000 × 12
= 5 : 6 : 7
Loss incurred = ₹1800
= ₹500
= ₹600
= ₹700
Question 5.
Dipu, Rabeya and Megha have started a small business by investing the capitals of ₹6500, ₹5200, ₹9100 respectively and just after one year they make a profit of ₹14,400. If they divided 
rd of the profit equally among themselves and the remaining in the ratio of their capitals, let us find the profit share of each.
Answer:
Dipu invested = ₹6500 for a year
Rabeya invested = ₹5200 for a year
Megha invested = ₹9100 for a year
Dipu’s total investment = ₹6500 × 12
Rabeya’s total investment = ₹5200 × 12
Megha’s total investment = ₹9100 × 12
Ratio of partnership = 6500 × 12 : 5200 × 12 : 9100 × 12
= 5 : 4 : 7
Total profit = ₹14,400
Profit which they divide equally among themselves 
= ₹9600
∴ Profit of each 
= ₹3200
Profit which they divide in the ratio of their capitals 
= ₹4800
Dipu's share of profit =
= ₹4500
Rabeya' s share of profit 
= ₹3600
Megha's share of profit 
= ₹6300
Hence,
Dipu’s total profit = ₹4500 + ₹3200
= ₹7700
Rabeya’s total profit = ₹3600 + ₹3200
= ₹6800
Megha’s total profit = ₹6300 + ₹3200
= ₹9500
Question 6.
Three friends have started a business by investing ₹8000, ₹10000 and ₹12000 respectively. They also took an amount as bank loan. At the end of year they made a profit of ₹13400. After paying the annual bank instalment of ₹5000 they divided the remaining money of the profit among themselves in the ratio of their capitals. Let us write by calculating the profit share of each.
Answer:
Given, 3 friends, say A, B and C, started a partnership business by investing ₹8000, ₹10000 and ₹12000 respectively for a year.
Ratio of partnership = 8000×12 : 10000×12 : 12000 × 12
= 4 : 5 : 6
Total profit = ₹13400
Annual bank instalment paid at the end of a year = ₹5000
∴ Remaining profit = ₹13400 - ₹5000
= ₹8400
= ₹2240
= ₹2800
= ₹3360
Question 7.
Three friends took loans of ₹6000, ₹8000 and ₹5000 respectively from a co-operative bank on the condition that they would not have to pay interest, if they would repay their loan within two years. They invested the money to purchase 4 cycle rickshaws. After two years they made a profit of ₹30400 excluding all the expenses. They divide the profit among themselves in the ratio of their capitals and repaid back their individual loans amount to the bank. Let us write by calculating the amount of their individual share and the ratio of their shares.
Answer:
Given, 3 friends, say A, B and C, started a partnership business by taking bank loan of ₹6000, ₹8000 and ₹5000.
Ratio of partnership = 6000 : 8000 : 5000
= 6 : 8 : 5
Total profit = ₹30400
= ₹9600
= ₹12800
= ₹8000
Hence, A’s, B’s and C’s share after they have returned their respective bank loan:
A’s share = ₹9600 - ₹6000
= ₹3600
B’s share = ₹12800 - ₹8000
= ₹4800
C’s share = ₹8000 - ₹5000
= ₹3000
Question 8.
Three friends invested ₹12000, ₹15000 and ₹110000 respectively to purchase a bus. The first person is a driver and the other are conductors. They decided to divide 
of the profit among themselves in the ratio of 3:2:2 according to their work and the remaining in the ratio of their capitals. If they earn ₹29260 in one month, let us find the share of each of them.
Answer:
Given, 3 friends, say A, B and C, started a partnership business by investing ₹12000, ₹15000 and ₹110000 respectively.
Ratio of partnership = 12000 : 15000 : 110000
= 12 : 15 : 110
They earn = ₹29260 in one month
Profit which they divide in the ratio of 3:2:2 according to their work 
= ₹11704
Hence, their shares in ratio of 3:2:2 are:
= ₹5016
= ₹3344
= ₹3344
Profit which they divide in the ratio of their capitals
= ₹17556
Hence, their shares in ratio of their capitals are:
= ₹5016
= ₹3344
= ₹3344
A’s share = ₹9600 - ₹6000
= ₹3600
B’s share = ₹12800 - ₹8000
= ₹4800
C’s share = ₹8000 - ₹5000
= ₹3000
Question 9.
Pradipbabu and Aminabibi started a business by investing ₹24000 and ₹30000 respectively at the beginning of a year. After 5 months Pradipbabu invested the capital of ₹4000 more. If the yearly profit was ₹27716, let us write by calculating the share of each of them.
Answer:
Pradipbabu’s initial investment = ₹24000 for a year
= 24000 × 12
= ₹288000
Later, Pradipbabu invested = ₹4000 for 7 months
= 4000×7
= ₹28000
So, Pradipbabu’s total investment = ₹288000 + ₹28000
= ₹316000
Aminabibi’s initial investment = ₹30000 for a year
= 30000×12
= ₹360000
Ratio of capital invested = 316000 : 360000
= 79:90
Total profit = ₹27716
Hence, their shares of profit in ratio of their capitals are:
= ₹12956
= ₹14760
Question 10.
Niyamat chacha and Karabi didi have started a partnership business together by investing ₹30000 and ₹50000 respectively. After 6 months Niyamat chacha has invested ₹40000 more but Karabi didi has withdrawn ₹10000 for personal need. If the profit at the end of the year is ₹19000, let us write by calculating the profit share of each of them.
Answer:
Niyamat chacha’s initial investment = ₹30000×12
= ₹360000
Karabi didi’s initial investment = ₹50000×12
= ₹600000
After 6 months Niyamat chacha has invested = ₹40000 more for 6 months.
= ₹40000×6
= ₹240000
So, Niyamat chacha’s total investment = ₹360000 + ₹240000
= ₹600000
After 6 months Karabi didi has withdrawn = ₹10000 for personal need.
= ₹10000×6
= ₹60000
So, Karabi didi’s total investment = ₹600000-₹60000
= ₹540000
Ratio of capital invested = 600000 : 540000
= 10:9
Total profit = ₹19000
Hence, their shares of profit in ratio of their capitals are:
= ₹10000
= ₹9000
Question 11.
Srikant and Soiffuddin invested ₹240000 and ₹30,0000 respectively at the beginning of the year to purchase a mini bus to run it on a route. After 4 months, their friend Peter joined them with a capital of ₹81000. Shrikant and Soiffuddin have withdrawn that money in the ratio of their capitals. Let us write by calculating the share of each if they make a profit of ₹39150 at the end of the year.
Answer:
Srikant’s investment = ₹240000×12 for a year
= ₹2880000
Soiffuddin’s investment = ₹300000×12 for a year
= ₹3600000
Peter’s investment = ₹81000×8, as he joined after 4 months.
= ₹648000
Ratio of capitals of Srikant, Soiffuddin and Peter respectively = 2880000 : 3600000 : 648000
= 40:50:9
Total profit = ₹39150
Hence, their shares of profit in ratio of their capitals are:
= ₹15818
= ₹19772
= ₹3559
Question 12.
Arun and Ajoy started a business jointly by investing ₹24000 and ₹30000 respectively at the beginning of the year. But after a few months Arun invested ₹12000 more. After a year, the profit was ₹14030 and Arun received the profit share of ₹7130. Let us find after how many months did does Arun invest money in that business.
Answer:
Arun’s initial investment = ₹24000×12
= ₹288000
Later, Arun has invested = ₹12000 more for x months.
= ₹12000x
Arun’s total invrstment = ₹288000 + ₹12000x
Ajoy’s total invrstment = ₹30000×12
= ₹360000
Total profit = ₹14030
Arun’s profit share = ₹7130
∴ Ajoy’s profit share = ₹14030-₹7130
= ₹6900
We know that ratio of profit share is equal to ratio of capital invested.
∴ Ratio of capital invested = Ratio of profit share = 7130:6900
= 713:690
6624 + 276x = 8556
276x = 8556-6624
276x = 1932
X = 7 months
∴ Arun invested money after = 12-7 = 5 months.
Question 13.
Three clay modellers from Kumartuli collectively took a loan of ₹100000 from a cooperative bank to set up a modelling workshop. They made a contract that after paying back the annual bank instalment of ₹28100, they would divide half of the profit among themselves in terms of the number of working days and the other half will be equally divided among them. Last year they worked 300 days, 275 days and 350 days respectively and made a profit of ₹139100. Let us write by calculating the share of each in this profit.
Answer:
Loan taken from is the investment made which is = ₹100000
Profit = ₹139100
Remaining profit, after paying back the annual bank instalment of ₹28100 = ₹139100-₹28100
= ₹111000
Given, 3 clay modellers, say A, B and C, decided to divide half of the profit among themselves in terms of the number of working days and the other half will be equally divided among them.
Half of Remaining profit which will be equally divided among them is 
Ratio of working days = 300 : 275 : 350
= 12 : 11 : 14
Hence, their shares in ratio of their working days are:
= ₹18000
= ₹16500
= ₹21000
A’s total share = ₹18000 + ₹18500
= ₹36500
B’s total share = ₹16500 + ₹18500
= ₹35000
C’s total share = ₹21000 + ₹18500
= ₹39500
Question 14.
Two friends invested ₹40000 and ₹50000 respectively to start a business. They made a contract that they would divide 50% of the profit equally among themselves and the remaining profit in the ratio of their capitals. Let us write the share of profit of the first friend if it is ₹800 less than that of the 2nd friend.
Answer:
Two friends, say A and B, invested ₹40000 and ₹50000 respectively to start a business.
Ratio of capital invested = 40000×12 : 50000×12
= 4:5
Let total profit be x.
Profit which is equally divided between them
Thus, profit of each 
Profit in ratio of their capitals:
Given, share of profit of the first friend is ₹800 less than that of the 2nd friend.
So,
X = 800×18
X = 14400
= ₹10400
Question 15.
Puja, Uttam and Meher started a partnership business with capitals of ₹5000, ₹7000 and ₹10000 respectively with the conditions that
(i) Monthly expense for running business is ₹125
(ii) Puja and Uttam each will get ₹200 for keeping the accounts. If the profit is ₹6960 at the end of the year, let us write by calculating the profit share each would get.
Answer:
Given, Monthly expense for running business is ₹125.
Puja’s investment = ₹5000×12 for a year
= ₹60000 + 125×12
= ₹60000 + 1500
= ₹61500
Uttam’s investment = ₹7000×12 for a year
= ₹84000 + 125×12
= ₹84000 + 1500
= ₹85500
Meher’s investment = ₹10000×12 for a year
= ₹120000 + 125×12
= ₹120000 + 1500
= ₹121500
Ratio of their capital = 61500 : 85500 : 121500
= 41:57:81
Total profit = ₹6960
Hence, their shares in ratio of their capital are:
= ₹1594
= ₹2216
= ₹3149
Question 16.
The capitals of three friends in a partnership business are ₹200, ₹150 and ₹250 respectively. After some time the ratio of their profit share will be
A. 5:3:4
B. 4:3:5
C. 3:5:4
D. 5:4:3
Answer:
Ratio of their capitals = 200:150:250
= 4:3:5
Question 17.
Suvendu and Noused started a business with capitals of ₹1500 and ₹1000. After a year there was a loss of ₹75. Then the loss of Suvendu is
A. ₹45
B. ₹30
C. ₹25
D. ₹40
Answer:
Ratio of their capitals = 1500:1000
= 3:2
Loss = ₹75
= ₹45
Question 18.
Fatima, Shreya and Smita started a business by investing total ₹6000. After a year Fatima, Shreya and Smita get profit share of ₹.50, ₹100 and ₹150 respectively. Smita invested in this business
A. ₹1000
B. ₹2000
C. ₹3000
D. ₹4000
Answer:
Given, profit share of ₹50, ₹100 and ₹150 of Fatima, Shreya and Smita respectively.
∴Ratio of their capital = 50:100:150
= 1:2:3
= ₹3000
Question 19.
Amal and Bimal started a business. Amal invested ₹500 for 9 months and Bimal invested some money for 6 months. If they make a profit of ₹69 in a year and Bimal gets profit share of ₹46. The capital of Bimal in the business is
A. ₹1500
B. ₹3000
C. ₹4500
D. ₹6000
Answer:
Given, Bimal’s profit share = ₹46
Bimal’s capital = 6x
Ratio of their capital = 500×6 : 6x
= 500 : x
46(500 + x) = 69x
23000 + 46x = 69x
69x-46x = 23000
23x = 23000
X = 1000
∴ Capital of Bimal in the business is = 1000 × 6
= ₹6000
Question 20.
Pallabi invested ₹500 for 9 months and Rajiya invested ₹600 for 5 months in a business. The ratio of their profit share will be
A. 3:2
B. 5:6
C. 6:5
D. 9:5
Answer:
Ratio of their profit share will be = 500×9 : 600×5
= 3 : 2
Question 21.
Let us write whether the following statements are true or false:
(i) At least 3 persons are needed in partnership business.
(ii) Ratio of capital of Raju and Ashif in a business is 5:4 and if Raju gets profit share of ₹80 of total profit, Ashif will get profit share of ₹100.
Answer:
(i) False
A business partnership always needs two or more people.
(ii) False
Ratio of profit share of Raju and Ashif respectively = 80 : 100
= 4 : 5
We know that ratio of profit share is equal to ratio of capital invested.
Thus, the above statement is false.
Question 22.
Let us fill in the blanks:
(i) Partnership business is _______types.
(ii) Without any other conditions in partnership business if the capitals of all the partners are invested for the same time, then such a business is called______.
(iii) Without any other conditions in partnership business, if the capitals of all the partners are invested for different time period, then such a business is called ______.
Answer:
(i) Two
(ii) Simple
(iii) Compound
Question 23.
In partnership business the ratio of capitals of Samir, Idrish and Antorny are as 
If they make a profit of ₹3700 at the end of the year, let us write by calculating profit share of Antony.
Answer:
= 10:12:15
Profit = ₹3700
= ₹1500
Question 24.
If a partnership business the ratio of capitals of Pritha and Rabeya is 2:3 and the ratio of Rabeya and Jesmin is 4:5, let us write by calculating the ratio of capitals of Pritha, Rabeya and Jesmin.
Answer:
Ratio of capitals of Pritha and Rabeya is = 2:3
Ratio of capitals of Rabeya and Jesmin is = 4:5
∴ ratio of capitals of Pritha, Rabeya and Jesmin = 2:3
= 4:5
= 8:12:15
Question 25.
The total profit is ₹1500 in a partnership business of two persons. If the capital of Rajib is ₹6000 and profit is ₹900, let us calculate how much was the capital of Abtab.
Answer:
Total profit is = ₹1500
Profit of Rajib = ₹900
∴ Profit of Abtab = ₹1500-₹900
= ₹600
Ratio of their profit = 900:600
= 3:2
We know that ratio of profit share is equal to ratio of capital invested.
= ₹600
Question 26.
The ratio of capitals of three persons is 3:8:5, and the profit of 1st person is ₹60 less of the 3rd person, let us calculate the total profit in this business.
Answer:
We know that ratio of profit share is equal to ratio of capital invested.
Ratio of capitals of three persons is = 3:8:5 .
∴ Ratio of profits of three persons is = 3:8:5
Given, profit of 1st person is ₹60 less of the 3rd person.
Let their profits be 3x, 8x and 5x.
5x-3x = 60
2x = 60
X = 30
Thus, Total profit = 3×30 + 8×30 + 5×30
= 90 + 240 + 150
= ₹480
Question 27.
Jayanta, Ajit and Kunal started partnership business investing ₹15000. At the end of the year, Jayanta, Ajit and Kunal received ₹800, ₹1000 and ₹1200 respectively as profit share. Let us calculate the amount of Jayanta’s capital that was invested in the business.
Answer:
Ratio of profit of Jayanta, Ajit and Kunal respectively = 800 : 1000 : 1200
= 4:5:6
We know that ratio of profit share is equal to ratio of capital invested.
= ₹4000