Ganit Prakash Class 10 Solutions Pdf In English
Chapter 14 Partnership Business Exercise 14.1
Application 1. Sulekha, Joynal, and Shibhu started a partnership business with a capital of Rs. 5,000, Rs. 4,500, and Rs. 7,000 respectively. If the profit is Rs. 11,550, at the end of the year, let us write by calculating the profit share by each of them
Solution: The ratio of capitals of Sulekha, Joynal & Shibu are = 5000:4500:7000 10: 9:14.
Total profit = Rs. 11,550.
∴ Out of Rs. 11500, Sulekha will get = 10 / 10+9+14 x 11500
= Rs. 3500.
Joynal will get = 9/10+9+14 x 11500
= Rs. 3150
& Shibu will get = 14 / 10+9+14 x 11500
= Rs. 4900.
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Application 2. Mitadidi, Sahanabibi, and Amal uncle of our village started a business jam-jelly with a capital of Rs. 15,000, Rs. 10,000, and Rs. 17,500. But at the end of the year loss is Rs. 4250. Let us write by calculating how much more each of them will have to pay.
Solution: In partnership business the ratio of investment of Mitadidi, Sahanabibi, and Amal uncle 15,000:10,000:17,500 = 6:4:7
Each partner shared their part of the loss in the ratio of their investment.
∴ In the loss of Rs. 4250, Mitadidi will pay = Rs. (7/6+4+7x 4250)
= Rs. 1,750.
In the loss of Rs. 4250, Sahanabibi will pay = Rs.(4/17 x4250)
= Rs. 1,000.
In the loss of Rs. 4250, Amal uncle will pay
= Rs. 1,500.
Ganit Prakash Class 10 Solutions Pdf In English
Application 3. Mariya and Shayam started a partnership business with a capital of Rs. 25,000 and 35,000 respectively with the conditions that :
1. 1/3rd of the total profit at first will be equally divided among them;
2. Later, the remaining profit will be divided into the ratio of their capital. If the profit at the end of the year is Rs. 36,000, let us find the share of profit each will get.
Solution:
1. of total profit will be equally divided i.e. Rs. 36,000 x-1/3) = Rs.
will be divided equally among Mariya and Shayam.
2. Remaining Rs. (36,000 – 12,000) = Rs. 24,000 will be divided in the ratio of their capitals.
Ratio of capitals of Mariya and Shayam = 25,000 : 35,000 = 5:7
∴ In the profit of Rs. 24,000 Mariya will get = Rs. (5/5+7 x 24000)
= Rs. 12000
In the profit of Rs. 24,000 Shayam will get = Rs. (7/5+7 x 24000)
= Rs. 14,000
∴ Mariya gets total = Rs. (12,000÷2+ 10,000) = Rs. 16,000.
Shayam gets total = Rs. (12,000÷2+14,000) = Rs. 20,000.
∴ According to the agreement, Mariya will get Rs. 16,000
and Shayam will get Rs. 20,000 of the profit of Rs. 36,000.
Application 4. Three retired persons invested Rs. 19,500, Rs. 27,300 and Rs. 15,600 respectively to set up a leather factory and after a year they had a profit of Rs. 43,200. If they divided 2/3 of this profit equally among themselves and of the remaining in the ratio of their capitals, let us find the share of each one of them.
Solution: Total profit was Rs. 43200, & they will divide 2/3 of this profit equally among themselves
i.e., each will get = Rs.(43200 x 2/3)
= Rs. 28,800.
Remaining profit = Rs. (43200 – 28800)
= Rs. 14,400
will divide among themselves in the ratio of their capitals.
Ratio of their capitals 19500: 27300 :15600 = 195 :273: 156 = 5:7:4
Out of the Remaining profit Rs. 14400
1st man will get = 5/5+7+4 x Rs. 14400
Rs. 5/16 x 14400 = Rs. 4500
2nd man will get = 7 / 5+7+4 x Rs. 14400
Rs. 7/16 x 14400 = Rs. 6300.
3rd man will get = 4 / 5+7+4 × Rs. 14400
= Rs.4/16 x 14400
= Rs. 3600.
∴ 1st man will get total amount = Rs. (28800 ÷ 3+ 4500)= Rs. (9600+ 4500)= Rs. 14100.
2nd man will get total amount = Rs. (28800 ÷ 3+ 6300) = Rs. (9600 + 6300) = Rs. 15900.
3rd man will get total amount = Rs. (28800+ 3+ 3600) = Rs. (9600+ 3600) Rs. 13200.
Application 5. Abhra, Tanbir, Amrita and Tathagata started a partnership business together with capital of Rs. 15,000, Rs. 21,000, Rs. 30,000 and Rs. 45,000 respectively with the condition that :
1 Abhra and Tanbir each partner will manage the business for a period of 6 months and each will get a share of 0.25 of the profit by dividing equally.
2. The remaining profit is to be divided among the four of them in the ratio of their capital. If the annual profit is Rs. 27232, let us write the share of each.
Solution:
1. Rs. (0.25 part of 27232) = Rs. 6808 will be equally divided among Abhra and Tanbir.
2. Rs. (27323 – 6808)= Rs. 20424 will be divided among them in the ratio of their capitals.
The ratio of capitals of Abhra, Tanbir, Amrita and Tathagata
= 15,000 :21,000 :30,000 :45,000 = 5 : 7: 10: 15
∴ The remaining part of the profit of Rs. 20424 will be divided among them in the ratio of their capital
Abhra will get = Rs. 5 / 5+7+10+15 x 20424 = Rs. 2760.
Similarly, in Rs. 20424, let us write by calculating how much money Tanbir, Amrita and Tathagata will get.
.. Abhra will get total = Rs. (6808÷ 2 +5/37 x 20424) = Rs. (3404 + 2760) = Rs. 6164.
Tanbir will get total = Rs. (6808 ÷ 2 + 7/37 x 20424) = Rs. (3404 +3864) = Rs. 7268.
Amrita will get = Rs. 10/37 x 20424 Rs. 5520
& Tathagata will get = Rs. 15 / 37 x 20424 Rs. 8280.
Ganit Prakash Class 10 Solutions Pdf In English
Application 6. Jaya aunty has started a small business of selling handcrafts with a capital of Rs. 10,000. After 6 months Sulekhadidi joined the business of Jaya aunty with a capital of Rs. 14,000. They make a profit of Rs. 5100. Let us write by calculating how much profit they will get.
Solution: At first the time for which the capital invested in this business of Jaya aunty and Sulekhadidi will be settled for an equal period.
Let Jaya aunty sells an object of Rs. 10,000 in 1 month and get a profit of Rs. x.
She sells an object for Rs. 10,000 in 2 months and gets a profit of Rs. 2x.
She sells objects for Rs. 10,000 in 12 months and gets a profit of Rs. 12x.
Jaya’s aunty has to make a profit equal to Rs. 12x in a month; she should have to invest Rs. 12 x 10,000 = Rs. 1,20,000.
Again, similarly if in one month, Sulekhadidi has to make a profit equal to that she earns the profit investing Rs. 14,000, for 6 months, she should have invested Rs. (6 x 14,000) = Rs. 84,000.
∴ The ratio of capitals of Jaya aunty and Sulekhadidi = Rs. 1,20,000:84,000 = 10: 7 The profit is divided in the ratio of capitals,
i.e., profit is divided in the ratio of 10: 7
∴ In profit of Rs. 5100 Jaya aunty will get = Rs. (10 / 10+7 x 5100) = Rs. 3,000.
In profit of Rs. 5100 Sulekhadidi will get = Rs.(7/10+7 x 5100) = Rs. 2,100.
Application 7. Manisha has started a business with a capital of Rs. 3750. After 6 months Rajat joined the business with a capital of Rs. 15,000. If at the end of the year, there was a loss of Rs. 6900, let us write by calculating the money each must pay to make up the loss.
Solution: Capital of Manisha = Rs. 3750 x 12 = Rs. 45,000
Capital of Rajat Rs. 15,000 x 6 = Rs. 90,000
The ratio of their capitals = Rs. 45,000: Rs. 90,000 1:2
Total loss = Rs. 6,900
∴Manisha will give = Rs. 1/3 × 6900 = Rs. 2,300
& Rajat will give = Rs. x 6900 Rs. 4,600.
WBBSE Solutions Guide Class 10
Application 8. Aminabibi, Ramenbabu and Ishitaunty of our village started a partnership business on the first of January of last year with capital of Rs. 50,000, Rs. 60,000 and Rs. 70,000 respectively. On the first of April, Ramenbabu invested Rs. 10,000 more money but on 1st of June Ishita aunty withdrew Rs. 10,000. If the total profit up to 13 December was Rs. 39240, let us write by calculating the profit share of each one of them on the basis of the ratio of their capitals.
Solution: Aminabibi has invested Rs. 50,000 for 12 months, if in a month she has to make a profit equal to that she gained in 12 months on that amount, she should invest Rs. (50,000 x 12),
i.e., Rs. 60,000.
Similarly, Ramenbabu has invested Rs. 60,000 for 3 months and Rs. (60,000 + 10,000),
i.e., 70,000 for 9 months.
Thus his investment on a monthly sale should be Rs. {(60,000 x 3) + (70,000 × 9)} = Rs. 8,10,000.
Again, Ishita aunty has invested Rs. 70,000 for 5 months and Rs. (70,000 – 10,000) =Rs. 60,000 for 7 months.
Thus her investment on a monthly scale should be = Rs. ((70,000 × 5) + (60,000 × 7)} = Rs. 7,70,000
The ratio of capitals of Aminabibi, Ramenbabu and Ishita aunty = 6,00,000 :8,10,000 :7,70,000 = 60: 81 : 77
∴ The proportional part of the share of Aminabibi, Ramenbabu and Ishita aunty in the ratio of their capitals are
60/218, 81/218 and 77/218 respectively.
Profit share is divided by the ratio of their capital.
∴ In the profit of Rs. 39240, Aminabibi will get = Rs. (60 / 218 x 39240) = Rs. 10,800
In the profit of Rs. 39240, Ramenbabu will get = Rs. (81 / 218 x 39240) = Rs. 14,580
In the profit of Rs. 39240, Ishita aunty will get = Rs. (77/218 x 39240) = Rs. 13,860
Application 9. Nivedita and Uma have started a business with capitals of Rs. 3,000 and Rs. 5,000 respectively. After 6 months Nivedita invested Rs. 4,000 more but after 6 months Uma withdrew Rs. 1,000. If the profit at the end of the year is Rs. 6,175, let us write by calculating the profit share of each of them.
Solution: Total Capital of Nivedita = Rs. (3000 12) + Rs. (4000 x 6)
= Rs. (36,000+ 24,000) Rs. 60,000.
Total Capital of Uma = Rs. (5,000 6) + Rs. (5,000 – 1,000) x 6
= Rs. (30,000+24,000) = Rs. 54,000
The ratio of the capital of Nivedita & Uma = Rs. 60,000: Rs. 54,000 = 60:54 = 10: 9
Total profit Rs. 6175.
Out of this profit, Nivedita will get = 10/19 x Rs. 6175 = Rs. 3250
& Uma will get = 9/19 x Rs. 6175 = Rs. 2925.
WBBSE Solutions Guide Class 10
Question 1. I and my friend Mala together have started a business with a capital of Rs. 15000 and Rs. 25000 respectively. If we make a profit of Rs.16,800 in a year, let us see the profit share we shall each get.
Solution: Ratio of my & Mala’s capital = Rs. 15,000: Rs. 25,000 = 15: 25 = 3:5
Total profit in a year = Rs. 16,800.
∴ My share of profit = 3 / 3+5 x Rs. 16,800
=3/8 x Rs. 16,800
= Rs. 6,300
& Mala’s share of profit = 5 / 3+5 x Rs. 16,800
= 5/8 x Rs. 16,800
= Rs. 10,500.
Question 2. Priyam, Supriya and Bullu have opened a small shop of a grocery shop with capital of Rs. 15000, Rs. 10000 and Rs. 25000 respectively. But after a year there was a loss of Rs. 3000. Let us write by calculating what each must pay to make up the loss.
Solution: Ratio of Priyam, Supriya &
Bulu’s capital = Rs. 15,000 :Rs. 10,000: Rs. 25,000 = 15: 10: 25 = 3:2:5
Total Loss = Rs. 3,000
To make up for the loss
Priyam will pay 2 / 3+2+5 x Rs. 3,000
= 3/10 Rs. 3,000
= Rs. 900.
Supriya will pay = 2 / 3+2+5 x Rs. 3,000 = Rs.
= Rs. 600.
Bulu will pay = 5 / 3+2+5 x Rs. 3,000 =
Rs. 5/10 x Rs. 3,000
= Rs. 1,500.
Question 3. Shobha and Masud together bought a car for Rs. 250000 and sold it for 262,500. If Sobha paid 1 ½ times more than Masud, let us write by calculating their shares of profit.
Solution: The sale price of a car is Rs. 2,62,500
Cost price of the car = Rs. 2,50,000
∴ Profit = Rs. (262500 – 250000) = Rs. 12,500.
Now, Ratio of Shobha’s & Masud’s capitals = 3/2 :1 = 3:2
∴ Shobha’s share of profit= 3 / 3+2 × Rs. 12,500
= 3/5 x Rs. 12,500
= Rs. 7,500
& Masud’s share of profit = 2/3 +2 x Rs. 12,500
= 2/5 x Rs. 12,500
= Rs. 5,000.
WBBSE Solutions Guide Class 10
Question 4. Three friends started a partnership business by investing Rs. 5000, Rs. 6000 and Rs. 7000 respectively. After running the business for one year, they found that there is a loss of Rs. 1800. They decided to pay to make up that loss to undisturbed their capital. Let us write by calculating the amount they have to pay.
Solution: Ratio of capitals of 3 friends = Rs. 5,000 Rs. 6,000 Rs. 7,000 5: 6:7.
Total loss Rs. 1,800.
1st friend will pay = 5 / 5+6+7 x Rs. 1,800
= 5/18 x Rs. 1,800
= Rs. 500.
2nd friend will pay = 6 / 5+6+7 x Rs. 1,800
= 6/18 x Rs. 1,800
= Rs. 600.
3rd friend will pay = 7 / 5+6+7 x Rs. 1,800
= 7/8 x Rs. 1,800
= Rs. 700.
Question 5. Dipu, Rabeya and Megha started a small business by investing capital of Rs. 6500, Rs. 5200, and Rs. 9100 respectively and just after one year they make a profit of 2/3 of Rs. 14,400. If they divided of the profit equally among themselves and the remaining in the ratio of their capitals, let us find the profit share of each.
Solution: Ratio of Dipu’s, Rabeya’s & Megha’s capitals
= Rs. 6500: Rs. 5200: Rs. 9100 = 65 : 52: 91=5:4:7
Total profit = Rs. 14400
2/3 of profit = 2/3 x Rs. 14400 = Rs. 9600.
∴ If Rs. 9600 is divided equally among themselves, each will get
= Rs. 9600 ÷ 3
= Rs. 3200.
The remaining amount of profit = Rs. (14400 – 9600)
= Rs. 4,800
∴ Rs. 4800 will be divided among themselves in their ratio of capitals.
.. Dipu will get = 5 / 5+4+7 x Rs. 4800
= 5/16 x Rs. 4800
= Rs. 1500.
Rabeya will get = 4 / 5+4+7 x Rs. 4800
= 4/16 x Rs. 4800
= Rs. 1200.
& Megha will get = 7 / 5+4+7 x Rs. 4800
= 7/16 x Rs. 4800
= Rs. 2100.
∴ Out of a total profit of Rs. 14400
Dipu’s share of profit = Rs. (3200 + 1500) = Rs. 4700.
Rabeya’s share of profit = Rs. (3200+ 1200)= Rs. 4400.
Megha’s share of profit = Rs. (3200+ 2100)= Rs. 5300.
Maths WBBSE Class 10 Solutions
Question 6. Three friends have started a business by investing Rs. 8000, Rs. 10000 and Rs. 12000 respectively. They also took an amount as a bank loan. At the end of the year, they made a profit of Rs. 13400. After paying the annual bank instalment of Rs. 5000 they divided the remaining money of the profit among themselves in the ratio of their capital. Let us write by calculating the profit share of each.
Solution: Ratio of the capital of three friends = Rs. 8000: Rs. 10000:Rs. 12000 = 8 :10 :12 = 4:56.
Total profit = Rs. 13400
Bank’s annual instalment = Rs. 5000
Remaining profit = Rs. (13400-5000) = Rs. 8400
∴Rs. 8400 will divide among themselves in the ratio of 4: 5: 6.
∴ 1st friend’s share of profit = 4 / 4+5+6 x Rs. 8400
= 4/15 x Rs. 8400
= Rs. 2240.
2nd friend’s share of profit = 5 / 4+5+6 x Rs. 8400
= 5/15 x Rs. 8400
= Rs. 2800.
3rd friend’s share of profit = 6 / 4+5+6 x Rs. 8400
= 6/15 x Rs. 8400
= Rs. 3360.
Question 7. Three friends took loans of Rs. 6000, Rs. 8000 and Rs. 5000 respectively from a cooperative 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 Rs. 30400 excluding all expenses. They divide the profit among themselves in the ratio of their capital and repaid back their individual loan amount to the bank. Let us write by calculating the amount of their individual share and the ratio of their shares.
Solution: Ratio of the capital of 3 friends = Rs. 6000: Rs. 8000: Rs. 5000
= 60: 80: 50
= 6: 8:5
Total profit Rs. 30400.
.: 1st friend’s share of profit = 6 / 6+8+5 x Rs. 30400
= 6/19 x Rs. 30400
= Rs. 9600.
2nd friend’s share of profit = 8/6+8+5 × Rs. 30400 =
8 / 19 x Rs. 30400 = Rs. 12800.
3rd friend’s share of profit = 5 / 6+8+5 x Rs. 30400
5/19 x Rs. 30400 = Rs. 8000.
Now they repaid back their individual loans to the bank.
∴ 1st friend’s share of profit Rs (96006000) = Rs. 3600.
2nd friend’s share of profit = Rs. (12C-8000) = Rs. 4800.
3rd friend’s share of profit = Rs. (8000-500; Rs. 3000.
The ratio of their remaining profit = Rs. 3600:Rs. 4800: Rs. 3000
= 36:48 :30
= 6: 8:5.
Question 8. Three friends invested Rs. 12000, Rs. 15000 and Rs. 110000 respectively to purchase a bus. The first person is a driver and the other two are conductors. They decided to divide 2/5th of the profit among themselves in the ratio of 3:2:2 according to their work and the remaining in the ratio of their capital. If they earn Rs. 29260 in one month, let us find the share of each of them.
Solution: Ratio of capitals of 3 friends = Rs. 12000: Rs. 15000: Rs. 11000 = 12:15:11
Total profit = Rs. 29260
They decided on 2/5 of the profit,
i.e., 2/5 x Rs. 29260
= Rs. 11704 will be divided among
themselves in the ratio of 3:2:2.
∴ 1st friend (Driver) will get = 3/7 x Rs. 11704
= Rs. 5016.
2nd friend (Conductor) will get =2/7 x Rs. 11704
= Rs. 3344
& 3rd friend (Conductor) will get = 2/7x Rs. 11704
= Rs. 3344.
Rest amount = Rs. (29260 – 11704)
= Rs. 1.1556 will be divided among themselves in the ratio of their capitals (i.e., 12 :15:11)
.: Driver will get = 12/38 x Rs. 11556
= Rs. 5544. (as 12+15+11=38)
1st Conductor will get = 15/38 x Rs. 11556
= Rs. 7930
2nd Conductor will get = 11/38 x Rs. 11556 = Rs. 5082
∴ The driver will get in total = Rs. (5016+ 5544) Rs. 10560.
1st Conductor will get in total = Rs. (3344+ 7930) = Rs. 10274.
2nd Conductor will get in total = Rs. (3344 + 5082) = Rs. 8426.
Question 9. Pradipbabu and Aminabibi started a business by investing Rs. 24000 and Rs. 30000 respectively at the begining of a year. After 5 months Pradipbabu invested capital of Rs. 4000 more. If the yearly profit was Rs. 27716, let us write by calculating the share of each of them.
Solution: Total capital of Pradipbabu throughout the year
= Rs. (24000 x 12 + 4000 x 7) = Rs. (288000+28000) = Rs. 316000
Total capital of Aminabibi = Rs. 30000 x 12 = Rs. 360000.
∴ The ratio of their capitals
Total profit = Rs. 27716.
Rs. 316000: Rs. 360000 316: 360
= 79: 90
∴ Share of profit of Pradipbabu = 79 / 79+90 x Rs. 27716 =
= 79 / 169 x Rs. 27716
= Rs. 12956.
Share of profit of Aminabibi = 90 / 79+90 x Rs. 27716
= 90 / 169 x Rs. 27716
= Rs. 14760.
Maths WBBSE Class 10 Solutions
Question 10. Niyamat chacha and Karabi didi have started a partnership business together by investing Rs. 30000 and Rs. 50000 respectively. After 6 months Niyamat chacha has invested Rs. 40000 more but Karabi didi has withdrawn Rs. 10000 for personal need. If the profit at the end of the year is Rs. 19000, let us write by calculating the profit share of each of them.
Solution: Total capital Niyamat Chacha throughout the year
= Rs. (30000 × 12+ 40000 x 6) = Rs. (360000+ 240000) = Rs. 600000
& Total capital of Karabi didi = Rs. (50000 x 6 + 40000 x 6) = Rs. (300000 + 240000) = Rs. 540000.
∴ Ratio of their capitals = Rs. 600000 :Rs. 540000 = 60:54
= 10: 9
Total profit Rs. 19000.
Share of profit of Niyamat Chacha = 10 / 10+9 x Rs. 19000
= 10/19 x Rs. 19000
Rs. 10000.
Share of profit of Karabi didi = 9 / 10+9 x Rs. 19000=
= 9 / 19 x Rs. 19000
= Rs. 9000.
Question 11. Srikant and Soiffuddin invested Rs. 240000 and Rs. 300000 respectively at the beginning of the year to purchase a minibus to run on a route. After 4 months, their friend Peter joined them with a capital of Rs. 81000. Srikant 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 Rs. 39150 at the end of the year.
Solution: Ratio of capitals of Srikant & Soiffuddin = Rs. 240000:Rs. 300000
= 24:30
= 4:5
After 4 months Peter joined them with a capital of Rs. 81000
& as this Rs. 81000 was withdrawn by Srikant & Soiffuddin in the ratio of their capitals.
∴Sritkant withdrawn = 4 / 4+5 x Rs. 81000
= Rs. 36000
& Saiffuddin withdrawn: = 5 / 4+5 x Rs. 81000 Rs. 45000.
∴Total Capital of Srikant for 1 year = Rs. [240000 x 4+ (240000-36000)]
= Rs. (960000+204000 8)
= Rs. (960000+ 1632000)
= Rs. 2592000.
Total Capital of Soiffuddin for 1 year = Rs. [300000 x 4+ (300000-45000) x 8]
= Rs. (1200000 25000 x 8)
= Rs. (1200000+ 2040000)
= Rs. 3240000
Total capital of Peter = Rs. 81000 × 8 = Rs. 648000
∴ The ratio of capital of Srikant, Soiffuddin & Peter
=2592000 3240000
= 648000
= 2592:3240 :648
= 72: 90: 18=4:5:1
Total profit = Rs. 39150
∴ Srikant’s share of profit = 4 / 4+5+1 x Rs. 39150=
= 4/10 x Rs. 39150
= Rs. 15660.
Soiffuddin’s share of profit = 5 / 4+5+1 x Rs. 39150
= 5/10 x Rs. 39150
= Rs. 19575.
Peter’s share of profit = 1/4+5+1 x Rs. 39150
= 1/10 X Rs. 39150
= Rs. 3915.
Maths WBBSE Class 10 Solutions
Question 12. Arun and Ajoy started a business jointly by investing Rs. 24000 and Rs. 30000 respectively at the beginning of the year. But after a few months, Arun invested Rs. 12000 more. After a year, the profit was Rs. 14030 and Arun received a profit share of Rs. 7130. Let us find out how many months Arun invest money in that business.
Solution: Let Arun invest Rs. 12,000 more after x months.
Arun’s Capital throughout the year
= Rs. [24000 x 12+12000 x (12-x)]
= Rs. (288000+ 144000 12000x)
= Rs. (432000 12000x).
ajoy’s Capital throughout the year
= Rs. 30000 x 12 = Rs. 360000
The ratio of Arun’s Capital & ajoy’s Capital
=(432000 12000x): 360000
= 1000(432 – 12x): 360000
= (432-12x): 360
= 12(36-x): 360
= (36x): 30
Total profit Rs. 14030.
∴ Arun’s share of profit = 36-x / (36-x)+30 x Rs. 14030.
= 36-x/66-x x Rs. 1.4030.
∴ According to the given problem,
14030 X 36-x / 66-x = 7130
or, 36-x / 66-x
= 7130/14030
= 713/1403
or, 713(66-x) = 1403(36-x)
or, 47058-713x = 50508-1403x
or, 1403x-713x= 50508-47058 or,
690x = 3450
..x = 3450 / 690
= 5
∴ After 5 months Arun invested Rs. 12,000 more.
Question 13. Three clay modellers from Kumartuli collectively took a loan of Rs. 100000 from a cooperative bank to set up a modelling workshop. They made a contract that after paying back the annual bank instalment of Rs. 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 Rs. 139100. Let us write by calculating the share of each in this profit.
Solution: Ratio of working days of 3 clay modellers
= 300 days: 275 days: 350 days = 12: 11: 14
Total profit Rs. 139100
They pay annual bank instalment = Rs. 28100
Remaining amount = Rs. (139100-28100) = Rs. 111000
1/2 of Rs. 111000 = Rs. 55500.
From Rs. 55500, each will get = Rs. (55500 ÷ 3)
= Rs. 18500
The rest Rs. 55500 will be divided among themselves in the ratio of 12: 11: 10.
∴ 1st man will get in total = Rs. (18500 + 12/37 x 555000) [12+11+ 14=37]
= Rs. (18500+ 18000)
= Rs. 36500
2nd man will get in total = Rs. (18500 + 11/37× 555000)
= Rs. (18500+ 16500) = Rs. 35000
3rd man will get in total = Rs. (18500 + 14/37 × 555000)
= Rs. (18500 +21000)
= Rs. 39500.
Question 14. Two friends invested Rs. 40000 and Rs. 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 capital. Let us write the share of profit of the first friend if it is Rs. 800 less than that of the 2nd friend.
Solution: Ratio of capitals of two friends = Rs. 40000 Rs. 50000 4:5
Let the total profit = Rs. x.
50% of Rs. x = Rs. x/2 will be divided among the two equally.
∴ Each will get = Rs. x/2 x ½
=Rs. x/4
Remaining Rs.( x-x/2) = Rs.
Rs. x/2 will be divided among them in the ratio of their capitals.
∴ 1st friend will get = 4/9 x Rs. x/2
= Rs. 2x/9
& 2nd friend will get 5/9 x Rs. x/2
= Rs. 5x/18
∴ In total
1st friend will get = Rs.(x/4 + 2x/9)
= Rs.9x+8x/36
= Rs. 17x/36
2nd friend will get = Rs. (x/4 +5x/18)
= Rs. 9x+10x / 36
= Rs.19x/36
∴ According to the problem,
19x/36 – 17x/36 = 800
or,2x/36 = 800
∴x = 800 x 36 / 2
∴ 1st friend will get = Rs.= Rs. 17 x 14400 / 36
= 6800
Question 15. Puja, Uttam and Meher started a partnership business with capitals of Rs. 5000, Rs. 7000 and Rs. 10000 respectively with the condition that
1. The monthly expense for running the business is Rs. 125;
2. Puja and Uttam each will get Rs. 200 for keeping the accounts. If the profit is Rs. 6960 at the end of the year, let us write by calculating the profit share each would get.
Solution: Ratio of Capitals of Puja: Uttam: Mehar
= Rs. 5000:Rs. 7000:Rs. 10000 = 5:7: 10
Total yearly expenses = Rs. 125 x 12 = Rs. 1500
For keeping the accounts Puja & Uttam will get yearly = Rs. (2 x 200) x 12 = Rs. 4800
Total profit= Rs. 6960.
Remaining profit after deducting expenses
= Rs. [6960 (1500+ 4800)]
= Rs. (69606300)
= Rs. 660
∴ Puka’s share of profit = 5/22 x Rs. 660 [5 +7 +10=22]
= Rs. 150.
Uttam’s share of profit=7/22 x Rs. 660
=Rs. 210.
Mehar’s share of profit = 10/22 x Rs. 660 Rs. 300.
∴ At the end of the year
Puja will get = Rs. (200 x 12 + 150)
= Rs. 2400 + 150
= Rs. 2550.
& Uttam will get = Rs. (200 x 12 + 210)
= Rs. 2400 + 210
= Rs. 2610.
Chapter 14 Partnership Business Exercise 14.1 Multiple Choice Question
Question 1. The capitals of three friends in a partnership business are Rs. 200, Rs. 150 and Rs. 250 respectively. After some time the ratio of their profit share will be
1. 5:3:4
2. 4:3:5
3. 3:5:4
4. 5:4:3
Solution: The ratio of capitals of 3 friends is = Rs. 200:Rs. 150: Rs. 250
= 20:15:25
= 4:3:5
Answer. 2. 4:3:5
Question 2. Suvendu and Nousad started a business with capital of Rs. 1500 and Rs. 1000. After a year there was a loss of Rs. 75. then the loss of Suvendu is
1. Rs. 45
2. Rs. 30
3. Rs. 25
4. Rs. 40
Solution: Ratio of capitals of Suvendu & Nousad Rs. 1500 Rs. 1000 3:2 Total loss = Rs. 75
.. Loss of Suvendu = 3/5x Rs. 75
= Rs. 45
Answer. 1. Rs. 45
Question 3. Fatima, Shreya and Smita started a business by investing a total of Rs. 6000. After a year Fatima, Shreya and Smita get profit share of Rs. 50, Rs. 100 and Rs. 150 respectively. Smita invested in this business.
1. Rs. 1000
2. Rs. 2000
3. Rs: 3000
4. Rs. 4000
Solution: Total Capital = Rs. 6000.
The ratio of profits = Rs. 50: Rs. 10: Rs. 150 = 1:2:3
∴ Ratio of Capitals = 1:2:3
∴ Smita’s Capital = 3 / 1+2+3 × Rs. 6000
= 3/6 x Rs. 6000
= Rs. 3000
Answer. 3. Rs. 3000
Question 4. Amal and Bimal started a business. Amal invested Rs. 500 for 9 months and Bimal invested some money for 6 months. They make a profit of Rs. 69 in a year and Bimal gets a profit share of Rs. 46. The capital of Bimal in the business is
1. Rs.1500
2. Rs. 3000
3. Rs. 4500
4. Rs. 6000
Solution: Let Bimal invest Rs. x for 6 months.
∴ Amal’s capital = Rs. 500 x 9 = Rs. 4500
& Bimal’s capital = Rs. x x 6
= Rs. 6x
Total profit Rs. 69
Bimal’s profit = Rs. 46 & Amal’s profit = Rs. (6946)= Rs. 23
Amal’s Capital / Bimal’s Capital = Amal’s Profit / Bimal’s Profit
or, Rs. 4500 / Rs. 6x
= Rs. 23 / Rs. 46
or, 4500/6x = 1/2
or, 6x = 2
4500 = 9000
∴ X = 9000/6
= 1500
Capital of Bimal = Rs. 1500
Answer. 1. Rs.1500
Question 5. Pallabi invested Rs. 500 for 9 months and Rajiya invested Rs. 600 for 5 months in a business. The ratio of their profit shares will be
1. 3:2
2. 5:6
3. 6:5
4. 9:5
Solution: Pallabi’s total capital = Rs. 500 x 9 = Rs. 4500
Rajiya’s total capital = Rs. 600 x 5 = Rs. 3000
The ratio of their capitals = Rs. 4500:Rs. 3000 = 3:2
∴ The ratio of their profits = 3:2
Answer. 1. 3:2
Chapter 14 Partnership Business Exercise 14.1 True Or False
1. At least 3 persons are needed in partnership business.
False
2. Ratio of capital of Raju and Ashif in a business is 5: 4 and if Raju gets a profit share of Rs. 80 of the total profit, Ashif will get a profit share of Rs. 100.
False
Chapter 14 Partnership Business Exercise 14.1 Fill In The Blanks
1. Partnership business is of Two types.
2. 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 Simple.
3. Without any other conditions in the partnership business, if the capitals of all the partners are invested for different time periods, then such a business is called a Compound.
Chapter 14 Partnership Business Exercise 14.1 Short Answer
Question 1. In the partnership business, the ratio of capitals of Samir, Idrish and Antony are as 1/6: 1/5: 1/4 If they make a profit of Rs. 3700 at the end of the year, let us write by calculating the profit share of Antony:
Solution. The ratio of capitals of Samir, Idrish & Antony
= 1/6 : 1/5 : 1/4
= (1/6 x 60) : (1/5 x 60) : (1/4 x 60)
= 10:12:15
Total profit = Rs. 3700
∴ Antony’s share of profit = 15 / 10+12+15 x Rs. 3700 =
= 15/37 x Rs. 3700
= Rs. 1500.
Question 2. If in 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.
Solution. Ratio of capitals of Pritha & Rabeya = 2:3 = 8:12
& Ratio of capitals of Rabeya & Jesmin = 4 :5 = 12:15
∴ Ratio Capitals of Pritha, Rabeya & Jesmin = 8: 12:15
Question 3. The total profit is Rs. 1500 in a partnership business of two persons. If the capital of Rajib is Rs. 6000 and the profit is Rs. 900, let us calculate how much capital Abtab is.
Solution. Total profit = Rs. 1500,
Rajib’s profit = Rs. 900
∴ Aftab’s profit = Rs.
(1500-900) = Rs. 600
Rajib’s Capital / Abtab’s Capital = Rajib’s Profit / Abtab’s Profit
= Rs. 6000 / Abtab’s Capital
= Rs. 900 / Rs. 600
= 3/2
∴ Aftab’s Capital = 3/2
Question 4. The ratio of capitals of three persons is 3: 8:5, and the profit of 1st person is Rs. 60 less than that of the 3rd person, let us calculate the total profit in this business.
Solution. The ratio of capitals of 3 people = 3:8:5
∴ Ratio of profit of 3 people = 3: 8:5
Let profit of 1st person = Rs. 3x
Profit of 2nd person = Rs. 8x
Profit of 3rd person = Rs. 5x
Total profit = Rs. (3x + 8x + 5x) = Rs. 16x
Now, 5x-3x= 60
or, 2x 60
∴ x = 30
Total profit = 16x
= Rs. 16 x 30
= Rs. 480.
Question 5. Jayanta, Ajit and Kunal started, a partnership business investing Rs. 15000. At the end of the year, Jayanta, Ajit and Kunal received Rs. 800, Rs. 1000 and Rs. 1200 respectively as profit shares. Let us calculate the amount of Jayanta’s capital that was invested in the business.
Solution. The ratio of profits of Jayanta, Ajit & Kunal
= Rs. 800:Rs. 1000:Rs. 1200
= 8:10:12
= 4:5:6
∴ Ratio of their capitals 4: 5: 6
Total capital = Rs. 15000
Jayanta’s capital = 4 / 4+5+6 x Rs. 15000 =
= 4/15 x Rs. 15000
= Rs. 4000.
