# Chapter – 14 : Partnership Business

 Book Name : Ganit Prakash Subject : Mathematics Class : 10 (Madhyamik) Publisher : Prof Nabanita Chatterjee Chapter Name : Partnership Business (14th Chapter)

Application 2.

Sulekha, Joynal and Shibhu started a partnership business with capitals of ₹ 5,000, ₹ 4,500 and ₹ 7,000 respectively. If the profit is ₹ 11,550, at the end of the year, let us write by calculating the profit share by each of them [Let me do it myself].

Solution:

Ratio of capitals of Sulekha, Joynal & Shibu are = 5000 : 4500 : 7000 = 10 : 9 : 14.

Total profit = ₹ 11,550.

\therefore Out of ₹ 11500, Sulekha will get = \frac{10}{10 + 9 + 14} × 11500 = ₹ 3500.

Joynal will get = \frac{9}{10 + 9 + 14} × 11500 = ₹ 3150

& Shibu will get = \frac{14}{10 + 9 + 14} × 11500 = ₹ 4900.

Application 3.

Mitadidi, Sahanabibi and Amal uncle of our village started a business of jam – jelly with capitals of ₹ 15,000, ₹ 10,000 and ₹ 17,500. But at the end of the year loss is ₹ 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 loss in the ratio of their investment.

\therefore In the loss of ₹ 4250, Mitadidi will pay = ₹ (\frac{7}{6 + 4 + 7} × 4250) = ₹ 1,750.

In the loss of ₹ 4250, Sahanabibi will pay = ₹ (\frac{4}{17} × 4250) = ₹ 1,000.

In the loss of ₹ 4250, Amal uncle will pay = ₹ 1,500.

Application 4.

Mariya and Shayam started a partnership business with capitals of ₹ 25,000 and 35,000 respectively with the conditions that :

(i) \frac{1}{3}rd of the total profit at first will be equally divided among them; (ii) Later, the remaining profit will be divided in the ratio of their capitals.

If the profit at the end of the year is ₹ 36,000, let us find the share of profit each will get.

Solution:

(i) \frac{1}{3} of total profit will be equally divided i.e. ₹ (36,000 × \frac{1}{3}) = ₹ will be divided equally among Mariya and Shayam.

(ii) Remaining ₹ (36,000 – 12,000) = ₹ 24,000 will be divided in the ratio of thell capitals.

Ratio of capitals of Mariya and Shayam = 25,000 : 35,000 = 5 : 7 \therefore In the profit of ₹ 24,000 Mariya will get = ₹ (\frac{5}{5 + 7} × 24,000) = ₹ 12,000

In the profit of ₹ 24,000 Shayam will get = ₹ (\frac{7}{5 + 7} × 24,000) = ₹ 14,000

\therefore Mariya gets total = ₹ (12,000 ÷ 2 + 10,000) = ₹ 16,000.

Shayam gets total = ₹ (12,000 ÷ 2 + 14,000) = ₹ 20,000.

\therefore According to agreement Mariya will get ₹ 16,000 and Shayam will get ₹ 20,000 of the profit ₹ 36,000.

Application 5.

Three retired persons invested Rs, 19,500, ₹ 27,300 and ₹ 15,600 respectively to set up a leather factory and after a year they had a profit of ₹ 43,200.

If they divided \frac{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. [Let me do it myself]

Solution:

Total profit was ₹ 43200, & they will divided \frac{2}{3} of this profit equally among themselves i.e., each will get = ₹ (43200 × \frac{2}{3}) = ₹ 28,800.

Remaining profit = ₹ (43200 – 28800) = ₹ 14,400 will divided among themselves in the ratio of their capitals.

Ratio of their capitals = 19500 : 27300 : 15600 = 195 : 273 : 156 = 5 : 7 : 4

Out of Remaining profit ₹ 14400

1st man will get = \frac{5}{5 + 7 + 4} × ₹ 14400

= ₹ \frac{5}{16} × 14400 = ₹ 4500

2nd man will get = \frac{7}{5 + 7 + 4} × ₹ 14400

= ₹ \frac{7}{16} × 14400 = ₹ 6300.

3rd man will get = \frac{4}{5 + 7 + 4} × ₹ 14400

= ₹ \frac{4}{16} × 14400 = ₹ 3600.

\therefore 1st man will get total amount = ₹ (28800 ÷ 3 + 4500) = ₹ (9600 + 4500) = ₹ 14100.

2nd man will get total amount = ₹ (28800 ÷ 3 + 6300) = ₹ (9600 + 6300) = ₹ 15900.

3rd man will get total amount = ₹ (28800 ÷ 3 + 3600) = ₹ (9600 + 3600) = ₹ 13200.

Application 6.

Abhra, Tanbir, Amrita and Tathagata started a partnership business together with capitals of ₹ 15,000, ₹ 21,000, ₹ 30,000 and ₹ 45,000 respectively with the condition that :

(i) 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. (ii) The remaining profit is to be divided among four of them in the ratio of their capitals. If the annual profit is ₹ 27232, let us write the share of each.

Solution:

(i) ₹ (0.25 part of 27232) = ₹ 6808 will be equally divided among Abhra and Tanbir.

(ii) ₹ (27323 – 6808) = ₹ 20424 will be divided among them in the ratio. of their capitals.

Ratio of capitals of Abhra, Tanbir, Amrita and Tathagata

= 15,000 : 21,000 : 30,000 : 45,000 = 5 : 7 : 10 : 15

\therefore Remaining part of profit of ₹ 20424 will be divided among them in the ratio of their capitals.

Abhra will get = ₹ \frac{5}{5 + 7 + 10 + 15} × 20424 = ₹ 2760.

Similarly, in ₹ 20424, let us write by calculating how much money Tanbir, Amrita and Tathagata will get.

\therefore Abhra will get total = ₹ (6808 ÷ 2 + \frac{5}{37} × 20424) = ₹ (3404 + 2760) = ₹ 6164

Tanbir will get total = ₹ (6808 ÷ 2 + \frac{7}{37} × 20424) = ₹ (3404 + 3864) = ₹ 7268

Amrita will get = ₹ \frac{10}{37} × 20424 = ₹ 5520

& Tathagata will get = ₹ \frac{15}{37} × 20424 ₹ 8280.

Application 7.

Jaya aunty has started a small business of selling handcrafts with a capital of ₹ 10,000. After 6 months Sulekhadidi joined the business of Jaya aunty with a capital of ₹ 14,000. They make a profit of ₹ 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 equal period.

Let Jaya anunty sells object of ₹ 10,000 in 1 month and gets a profit of ₹ x.

She sells object of ₹ 10,000 in 2 months and get a profit of ₹ 2x.

She sells object of ₹ 10,000 in 12 months and get a profit of ₹ 12x.

Jaya aunty has to make a profit equals to ₹ 12x in a month; she should have to invest ₹ 12 × 10,000 = ₹ 1,20,000.

Again, similarly if in one month, Sulekhadidi has to make a profit equal to that she earns the profit investing ₹ 14,000, for 6 months, she should have invested ₹ (6 × 14,000) = ₹ 84,000

₹ 84,000. The ratio of capitals of Jaya aunty and Sulekhadidi = ₹ 1,20,000 : 84,000 = 10 : 1

The profit is divided in the ratio of The profit is divided in the ratio of capitals, i.e., profit is divided in the ratio of 10 : 7 \therefore In profit of ₹ 5100 Jaya aunty will get = ₹ (\frac{10}{10 + 7} × 5100) = ₹ 3,000.

In profit of ₹ 5100 Sulekhadidi will get = ₹ (\frac{7}{10 + 7} × 5100) = ₹ 2,100.

Application 8.

Manisha has started a business with a capital of ₹ 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 ₹ 6900, let us write by calculating make up the loss. [Let me do it myself]

Solution:

Capital of Manisha = ₹ 3750 × 12 = ₹ 45,000

Capital of Rajat = ₹ 15,000 × 6 = ₹ 90,000

Ratio of their capitals = ₹ 45,000 : ₹ 90,000 = 1 : 2

Total loss = ₹ 6,900

Manisha will give = ₹ \frac{1}{3} × 6900 = ₹ 2,300

& Rajat will give = ₹ \frac{2}{3} × 6900 = ₹ 4,600.

Application 9.

Aminabibi, Ramenbabu and Ishitaunty of our village started a partnership business on first January of last year with capitals of ₹ 50,000, ₹ 60,000 and ₹ 70,000 respectively. On first April, Ramenbabu invested ₹ 10,000 more money but on 1st June Ishita aunty withdrew ₹ 10,000. If the total profit upto 13 December was ₹ 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 ₹ 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 ₹ (50,000 × 12), i.e., ₹ 60,000.

Similarly, Ramenbabu has invested ₹ 60,000 for 3 months and ₹ (60,000 + 10,000), i.e., 70,000 for 9 months. Thus his investment on a monthly sale should be ₹ \{(60,000 × 3) + (70,000 × 9)\} = ₹ 8,10,000.

Again, Ishita aunty has invested ₹ 70,000 for 5 months and ₹ (70, 000 – 10,000) = ₹ 60,000 for 7 months.

Thus her investment on a monthly scale should be = ₹\{(70,000 × 5) + (60,000 × 7)\} = ₹ 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

\therefore The proportional part of share of Aminabibi; Ramenbabu and Ishita aunty in the ratio of their capitals are \frac{60}{218}, \frac{81}{218} \text{ and } \frac{77}{218} respectively.

Profit share is divided in the ratio of their capitals.

\therefore In the profit of ₹ 39240, Aminabibi will get = ₹ (\frac{60}{218} × 39240) = ₹ 10,800 In the profit of ₹ 39240, Ramenbabu will get = ₹ (\frac{81}{218} × 39240) = ₹ 14,580

In the profit of ₹ 39240, Ishita aunty will get = ₹ (\frac{77}{218} × 39240) = ₹ 13,860.

Application 10.

Nivedita and Uma have started a business with capitals of ₹ 3,000 and ₹ 5,000 respectively. After 6 months Nivedita invested ₹ 4,000 more but after 6 months Uma withdrew ₹ 1,000. If the profit at the end of the year is ₹ 6,175, let us write by calculating the profit share of each of them. [Let me do it myself]

Solution:

Total Capital of Nivedita = ₹ (3000 12) + ₹ (4000 × 6)

= ₹ (36,000 + 24,000) = ₹ 60,000.

Total Capital of Uma = ₹ (5,0006) + ₹ (5,000 – 1,000) × 6

= ₹ (30,000 + 24,000) = ₹ 54,000

Ratio of capital of Nivedita & Uma = ₹ 60,000 : ₹ 54,000 = 60 : 54 = 10 : 9

Total profit = ₹ 6175. Out of this profit, Nivedita will ‘get = \frac{10}{19} × ₹ 6175 = ₹ 3250

& Uma will get = \frac{9}{19} × ₹ 6175 = ₹ 2925.

## LET US SEE BY CALCULATING – 14

Question 1

I and my friend Mala together have started a business with capital of ₹ 15000 and ₹ 25000 respectively. If we make a profit of ₹16,800 in a year, let us see the profit share we shall each get.

Solution:

Ratio of my & Mala’s capital = ₹ 15,000 : ₹ 25,000 = 15 : 25 = 3 : 5

Total profit in a year = ₹ 16,800.

\therefore My share of profit = \frac{3}{3 + 5} × ₹ 16,800 = \frac{3}{8} × ₹ 16,800 = ₹ 6,300

& Mala’s share of profit = \frac{5}{3 + 5} × ₹ 16,800 = \frac{5}{8} × ₹ 16,800 = ₹ 10,500.

Question 2

Priyam, Supriya and Bullu 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.

Solution:

Ratio of Priyam, Supriya & Bulu’s capital = ₹ 15,000 : ₹ 10,000 : ₹ 25,000 = 15 : 10 : 25 = 3 : 2 : 5

Total Loss = ₹ 3,000

To make up loss –

Priyam will pay = \frac{2}{3 + 2 + 5} × ₹ 3,000 = \frac{3}{10} ₹ 3,000 = ₹ 900

Supriya will pay = \frac{2}{3 + 2 + 5} × ₹ 3,000 = ₹ \frac{2}{10} × ₹ 3,000 = ₹ 600

Bulu will pay = \frac{5}{3 + 2 + 5} × ₹ 3,000 = ₹ \frac{5}{10} × ₹ 3,000 = ₹ 1,500.

Question 3

Shobha and Masud together bought a car for ₹ 250000 and sold it for 262,500. If Sobha paid 1 \frac{1}{2} times more than Masud, let us write by calculating their shares of profit.

Solution:

Sale price of a car = ₹ 2,62,500

Cost price of the car = ₹ 2,50,000

∴ Profit = ₹ (262500 – 250000) = ₹ 12,500

Now, Ratio of Shobha’s & Masud’s capitals = \frac{3}{2} : 1 = 3 : 2

\therefore Shobha’s share of profit = \frac{3}{3 + 2} × ₹ 12,500 = \frac{3}{5} × ₹ 12,500 = ₹ 7,500

& Masud’s share of profit = \frac{2}{3 + 2} × ₹ 12,500 = \frac{2}{5} × ₹ 12,500 = ₹ 5,000.

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 undisturbed their capitals. Let us write be calculating the amount they have to pay.

Solution:

Ratio of capitals of 3 friends = ₹ 5,000 : ₹ 6,000 : ₹ 7,000 = 5 : 6 : 7

Total loss = ₹ 1,800.

1st friend will pay = \frac{5}{5 + 6 + 7} × ₹ 1,800

= \frac{5}{18} × ₹ 1,800

= ₹ 500.

2nd friend will pay = \frac{6}{5 + 6 + 7} × ₹ 1,800

= \frac{6}{18} × ₹ 1,800

= ₹ 600.

3rd friend will pay = \frac{7}{5 + 6 + 7} × ₹ 1,800

= \frac{7}{18} × ₹ 1,800

= ₹ 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 \frac{2}{3} \mathrm{rd} 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

= ₹ 6500 : ₹ 5200 : ₹ 9100 = 65 : 52 : 91 = 5 : 4 : 7

Total profit = ₹ 14400

\frac{2}{3} of profit = \frac{2}{3} × ₹ 14400 = ₹ 9600.

\therefore If ₹ 9600 divided equally among themselves, each will get

= ₹ 9600 ÷ 3 = ₹ 3200.

Remaining amount of profit = ₹ (14400 – 9600) = ₹ 4,800

\therefore ₹ 4800 will be divided among themselves in their ratio of capitals.

\therefore Dipu will get = \frac{5}{5 + 4 + 7} × ₹ 4800 = \frac{5}{16} × ₹ 4800 = ₹ 1500.

Rabeya will get = \frac{4}{5 + 4 + 7} × ₹ 4800 = \frac{4}{16} × ₹ 4800 = ₹ 1200

& Megha will get = \frac{7}{5 + 4 + 7} × Rs : 4800 = \frac{7}{16} × ₹ 4800 = ₹ 2100.

\therefore Out of total profit of ₹ 14400 :

Dipu’s share of profit = ₹ (3200 + 1500) = ₹ 4700.

Rabeya’s share of profit = ₹ (3200 + 1200) = ₹ 4400.

Megha’s share of profit = ₹ (3200 + 2100) = ₹ 5300.

Question 6

Three friends have started a business by investing ₹ 8000, Rs, 10000 and Rs 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.

Solution:

Ratio of capital of three friends = ₹ 8000 : ₹ 10000 : ₹ 12000

= 8 : 10 : 12 = 4 : 5 : 6.

Total profit = ₹ 13400

Bank’s annual instalment = ₹ 5000

Remaining profit = ₹ (13400 – 5000) = ₹ 8400

\therefore ₹ 8400 will divided among themselves in the ratio of 4 : 5 : 6.

\therefore 1st friend’s share of profit = \frac{4}{4 + 5 + 6} × ₹ 8400 = \frac{4}{15} × ₹ 8400 = ₹ 2240.

2nd friend’s share of profit = \frac{5}{4 + 5 + 6} × ₹ 8400 = \frac{5}{15} × ₹ 8400 = ₹ 2800.

3rd friend’s share of profit = \frac{6}{4 + 5 + 6} × ₹ 8400 = \frac{6}{15} × ₹ 8400 = ₹ 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 yea₹ They invested the money to purchase 4 cycle rickshaws. After two years they made a profit of ₹ 30400 excluding all the expenses. They divides 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 theiı ińdividual share and the ratio of their shares.

Solution:

Ratio of capital of 3 friends = ₹ 6000 : ₹ 8000 : ₹ 5000 = 60 : 80 : 50 = 6 : 8 : 5

Total profit = ₹ 30400.

\therefore 1st friend’s share of profit = \frac{6}{6 + 8 + 5} × ₹ 30400 = \frac{6}{19} × ₹ 30400 = ₹ 9600.

2nd friend’s share of profit = \frac{8}{6 + 8 + 5} × ₹ 30400 = \frac{8}{19} × ₹ 30400 = ₹ 12800.

3rd friend’s share of profit = \frac{5}{6 + 8 + 5} × ₹ 30400 = \frac{5}{19} × ₹ 30400 = ₹ 8000.

Now they repaid back their individual loans to the bank.

\therefore 1st friend's share of profit = ₹ (9600 - 6000) = ₹ 3600.

2nd friend's share of profit = ₹ (12800 - 8000) = ₹ 4800.

3rd friend's share of profit = ₹ (8000 - 5000) = ₹ 3000.

\therefore Ratio of their remaining profit = ₹ 3600 : ₹ 4800 : ₹ 3000

= 36 : 48 : 30 = 6 : 8 : 5

Question 8

Three friends invested ₹ 12000, ₹ 15000 and ₹ 110000 respectively to purchase a bus. The first person is a driver and ₹ 110000 respectively to predecided to divide \frac{2}{5} th 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 them.

Solution:

Ratio of capitals of 3 friends = ₹ 12000 : ₹ 15000 : ₹ 110000 = 12 : 15 : 11

Total profit = ₹ 29260

They decided \frac{2}{5} of the profit, i.e., \frac{2}{5} × ₹ 29260 = ₹ 11704 will be divided among themselves in the ratio of 3 : 2 : 2.

1st friend (Driver) will get = \frac{3}{7} × ₹ 11704 = ₹ 5016.

2nd friend (Conductor) will get = \frac{2}{7} × ₹ 11704 = ₹ 3344

& 3rd friend (Conductor) will get = \frac{2}{7} × ₹ 11704 = ₹ 3344.

Rest amount = ₹ (29260 - 11704) = ₹ 11556 will be divided among themselves in the ratio of their capitals (i.e., 12 : 15 : 11 )

\therefore Driver will get = \frac{12}{38} × ₹ 11556 = ₹ 5544. ( as 12 + 15 + 11 = 38)

1st Conductor will get = \frac{15}{38} × ₹ 11556 = ₹ 7930

2nd Conductor will get = \frac{11}{38} × ₹ 11556 = ₹ 5082

\therefore Driver will get in total = ₹ (5016 + 5544) = ₹ 10560.

1st Conductor will get in total = ₹ (3344 + 7930) = ₹ 10274.

2nd Conductor will get in total = ₹ (3344 + 5082) = ₹ 8426.

Question 9

Pradipbabu and Aminabibi started a business by investing ₹ 24000 and ₹ 30000 respectively at the begining of the 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.

Solution:

Total capital of Pradipbabu throughout the year

= ₹ (24000 × 12 + 4000 × 7) = ₹ (288000 + 28000) = ₹ 316000

Total capital of Aminabibi = ₹ 30000 × 12 = ₹ 360000.

\therefore Ratio of their capitals = ₹ 316000 : ₹ 360000 = 316 : 360 = 79 : 90

Total profit = ₹ 27716.

\therefore Share of profit of Pradipbabu = \frac{79}{79 + 90} × ₹ 27716 = \frac{79}{169} × ₹ 27716 = ₹ 12956.

Share of profit of Aminabibi = \frac{90}{79 + 90} × ₹ 27716 = \frac{90}{169} × ₹ 27716 = ₹ 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 needs. If the profit at the end of the year is ₹ 19000, let us write by calculating the profit share of each of them.

Solution:

Total capital Niyamat Chacha throughout the year

= ₹ (30000 × 12 + 40000 × 6) = ₹ (360000 + 240000) = ₹ 600000

& Total capital of Karabi didi = ₹ (50000 × 6 + 40000 × 6) = ₹ (300000 + 240000)

= ₹ 540000.

\therefore Ratio of their capitals = ₹ 600000 : ₹ 540000 = 60 : 54 = 10 : 9

Total profit = ₹ 19000.

Share of profit of Niyamat Chacha = \frac{10}{10 + 9} × ₹ 19000 = \frac{10}{19} × ₹ 19000. ₹ 10000.

Share of profit of Karabi didi = \frac{9}{10 + 9} × ₹ 19000 = \frac{9}{19} × ₹ 19000 = ₹ 9000.

Question 11

Srikant and Soiffuddin invested ₹ 240000 and ₹ 300000 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 captial of ₹ 81000 . Srikant and Solffuddin 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.

Solution:

Ratio of capitals of Srikant & Soiffuddin = ₹ 240000 : ₹ 300000 = 24 : 30 = 4 : 5

After 4 months Peter joined them with a capital of ₹ 81000

& as this ₹ 81000 was withdrawn by Srikant & Soiffuddin in the ratio of their capitals.

\therefore Sritkant withdrawn = \frac{4}{4 + 5}× ₹ 81000 = ₹ 36000

& Saiffuddin withdrawn = \frac{5}{4 + 5} × ₹ 81000 = ₹ 45000

\therefore Total Capital of Srikant for 1 year = ₹ [240000 × 4 + (240000 - 36000)]

= ₹ (960000 + 204000 8) = ₹ (960000 + 1632000) = ₹ 2592000.

Total Capital of Soiffuddin for 1 year = ₹ [300000 × 4 + (300000 - 45000) × 8]

= ₹ (1200000 + 25000 × 8)

= ₹ (1200000 + 2040000)

= ₹ 3240000

Total captial of Peter = ₹ 81000 × 8 = ₹ 648000

\therefore Ratio of capital of Srikant, Soiffuddin & Peter

= 2592000 : 3240000 : 648000

= 2592 : 3240 : 648 = 72 : 90 : 18 = 4 : 5 : 1

Total profit = ₹ 39150

\therefore Srikant's share of profit = \frac{4}{4 + 5 + 1} × ₹ 39150 = \frac{4}{10} × ₹ 39150 = ₹ 15660.

Soiffuddin's share of profit = \frac{5}{4 + 5 + 1} × ₹ 39150 = \frac{5}{10} × ₹ 39150 = ₹ 19575.

Peter's share of profit = \frac{1}{4 + 5 + 1} × ₹ 39150 = \frac{1}{10} × ₹ 39150 = ₹ 3915.

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 Rs 12000 more. After a year. the profit was Rs 14030 and Arun received the profit share of Rs 7130. Let us find out how many months Arun invested money in that business.

Solution:

Let Arun invested ₹ 12,000 more after x months.

Arun's Capital throughout the year

= ₹ [24000 × 12 + 12000 × (12 - x)]

= ₹ (288000 + 144000 - 12000 x) = ₹ (432000 - 12000 x)

Ajoy's Capital throughout the year

= ₹ 30000 × 12 = ₹ 360000

Ratio of Arun's Capital & Ajoy's Capital

= (432000 - 12000 x) : 360000

= 1000(432 - 12 x) : 360000

= (432 - 12 x) : 360 = 12(36 - x) : 360 = (36 - x) : 30

Total profit = ₹ 14030. \therefore Arun's share of profit = \frac{36 - x}{(36 - x) + 30} × ₹ 14030.

= \frac{36 - x}{66 - x} × Rs : 14030.

\therefore According to the given problem,

14030 × \frac{36 - x}{66 - x} = 7130

or, \frac{36 - x}{66 - x} = \frac{7130}{14030} = \frac{713}{1403}

or, 713(66 - x) = 1403(36 - x)

or, 47058 - 713x = 50508 - 1403x

or, 1403x - 713x = 50508 - 47058

or, 690x = 3450

\therefore x = \frac{3450}{690} = 5

\therefore After 5 months Arun invested ₹ 12,000 more.

Question 13

Three clay modellers from Kumartuli collectively took a loan of ₹ 100000 from a co-operative 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.

Solution:

Ratio of working days of 3 clay modellers

= 300 days : 275 days : 350 days = 12 : 11 : 14

Total profit = ₹ 139100

They pay annual bank instalment = ₹ 28100

Remaining amount = ₹ (139100 - 28100) = ₹ 111000

\frac{1}{2} of ₹ 111000 = ₹ 55500.

From ₹ 55500, each will get = ₹ (55500 ÷ 3) = ₹ 18500

Rest ₹ 55500 will be divided among themselves in the ratio of 12 : 11 : 10.

\therefore 1st man will get in total = ₹ (18500 + \frac{12}{37} × 555000) [12 + 11 + 14 = 37]

= ₹ (18500 + 18000) = ₹ 36500

2nd man will get in total = ₹ (18500 + \frac{11}{37} × 555000)

= ₹ (18500 + 16500) = ₹ 35000

3rd man will get in total = ₹ (18500 + \frac{14}{37} × 555000)

= ₹ (18500 + 21000) = ₹ 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 them. selves 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.

Solution:

Ratio of capitals of two friends = ₹ 40000 : ₹ 50000 = 4 : 5

Let the total profit = ₹ x.

50% of ₹ x = ₹ \frac{x}{2} will be divided among the two equally.

\therefore Each will get = ₹ \frac{x}{2} × \frac{1}{2} = \text{ ₹ }\frac{x}{4}

Remaining ₹ (x - \frac{x}{2}) = ₹

\frac{x}{2} will be divided among them in the ratio of their capitals.

\therefore 1st friend will get = \frac{4}{9} × ₹ \frac{x}{2} = \text{ ₹ } \frac{2 x}{9}

& 2nd friend will get = \frac{5}{9} × \text{ ₹ } \frac{x}{2} = \text{ ₹ } \frac{5 x}{18}

\therefore In total : -

1st friend will get = \text{ ₹ } (\frac{x}{4} + \frac{2 x}{9}) = \text{ ₹ } \frac{9 x + 8 x}{36} = \text{ ₹ } \frac{17 x}{36}

2nd friend will get = \text{ ₹ } (\frac{x}{4} + \frac{5 x}{18}) = \text{ ₹ } \frac{9 x + 10 x}{36} = \text{ ₹ } \frac{19 x}{36}

\therefore According to the problem,

\frac{19 x}{36} - \frac{17 x}{36} = 800

or, \frac{2 x}{36} = 800

\therefore x = \frac{800 × 36}{2} = ₹ 14400

\therefore 1st friend will get = ₹ \frac{17 × 14400}{36} = 6800. Ans.

Question 15

Puja, Uttam and Meher started a partnership business with a capital of ₹ 5000, ₹ 7000 and ₹ 10000 respectively with the conditions that (i) Monthly expense for running the business is ₹ 125; (ii) Puja and Uttam each will get Rs 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.

Solution:

Ratio of Capitals of Puja : Uttam : Mehar

₹ 5000 : ₹ 7000 : ₹ 10000 = 5 : 7 : 10

Total yearly expenses = ₹ 125 × 12 = ₹ 1500

For keeping the accounts Puja & Uttam will get yearly = ₹ (2 × 200) × 12 = ₹ 4800

Total profit = ₹ 6960

Remaining profit after deducting expenses

= ₹ [6960 - (1500 + 4800)] = Rs : (6960 - 6300) = ₹ 660

\therefore Puka's share of profit = \frac{5}{22} × ₹ 660 = ₹ 150. [5 + 7 + 10 = 22]

Uttam's share of profit = \frac{7}{22} × ₹ 660 = ₹ 210.

Mehar's share of profit = \frac{10}{22} × ₹ 660 = ₹ 300.

\therefore At the end of the year

Puja will get = ₹ (200 × 12 + 150) = ₹ 2400 + 150 = ₹ 2550.

& Uttam will get = ₹ (200 × 12 + 210) = ₹ 2400 + 210 = ₹ 2610.

## Very Short Answer : (V.S.A.)

(A) M.C.Q :

Question 1

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

1. 5 : 3 : 4
2. 4 : 3 : 5
3. 3 : 5 : 4
4. 5 : 4 : 3

Solution:

Ratio of capitals of 3 friends is = ₹ 200 : ₹ 150 : ₹ 250 = 20 : 15 : 25 = 4 : 3 : 5

Ans. (b) 4 : 3 : 5

Question 2

Suvendu and Nousad started a business with capitals of ₹ 1500 and ₹ 1000. After a year there was a loss of ₹ 75. then the loss of Suvendu is

1. ₹ 45
2. ₹ 30
3. ₹ 25
4. ₹ 40

Solution:

Ratio of capitals of Suvendu & Nousad = ₹ 1500 : ₹ 1000 = 3 : 2

Total loss = ₹ 75

\therefore Loss of Suvendu = \frac{3}{5} × ₹ 75 = ₹ 45

Ans. (a) ₹ 45

Question 3

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.

1. ₹ 1000
2. ₹ 2000
3. ₹ 3000
4. ₹ 4000

Solution:

Total Capital = ₹ 6000.

Ratio of profits = ₹ 50 : ₹ 10 : ₹ 150 = 1 : 2 : 3

\therefore Ratio of Capitals = 1 : 2 : 3

\therefore Smita's Capital = \frac{3}{1+2+3} × ₹ 6000 = \frac{3}{6} × ₹ 6000 = ₹ 3000

Ans. (c) ₹ 3000

Question 4

Amal and Bimal started a business. Amal invested ₹ 500 for 9 months and Bimal invested some money for 6 months. They make a profit of ₹ 69 in a year and Bimal gets a profit share Rs 46. The capital in the business is

1. ₹ 1500
2. ₹ 3000
3. ₹ 4500
4. ₹ 6000

Solution:

Let Bimal invested ₹ × for  6 months. \therefore Amal's capital = ₹ 500 × 9 = ₹ 4500

& Bimal's capital = ₹ x × 6 = ₹ 6 x

Total profit = ₹ 69

Bimal's profit = ₹ 46 & Amal's profit = ₹ (69-46) = ₹ 23

\therefore \frac{\text { Amal's Capital }}{\text { Bimal's Capital }} = \frac{\text { Amal's Profit }}{\text { Bimal's Profit }}

or, \frac{\text { ₹ } 4500}{\text { ₹ } 6 x} = \frac{\text { ₹ } 23}{\text { ₹ } 46} \text{ or, } \frac{4500}{6 x} = \frac{1}{2} \quad or, 6x = 2, 4500 = 9000

\therefore x = \frac{9000}{6} = 1500 \quad \therefore Capital of Bimal = ₹ 1500

Ans. (a) ₹ 1500

Question 5

Pallabi invested ₹ 500 for 9 months and Rajiya invested ₹ 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 = ₹ 500 × 9 = ₹ 4500

Rajiya's total capital = ₹ 600 × 5 = ₹ 3000

Ratio of their capitals = ₹ 4500 : ₹ 3000 = 3 : 2

\therefore Ratio of their profits = 3 : 2

Ans. (a) 3 : 2

(B) Let us write whether the following statements are true or false :

Question 1

At least 3 persons are needed in partnership business.

Solution:

FALSE

Question 2

Ratio of capitals 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.

Solution:

FALSE

(C) Let us fill in the blanks :

Question 1

Partnership business is of ________________ types.

Solution:

Two.

Question 2

Without any other conditions in partnership business if the capitals of all the ______________________.

Solution:

Simple.

Question 3

Without any other conditions in partnership business, if the capitals of all the partners are invested for different time periods, then such a business is called _________________.

Solution:

Compound.

## Short answer type questions : (S.A.)

Question 1

In partnership business the ratio of capitals of Samir, Idrish and Antony are as \frac{1}{6} : \frac{1}{5} : \frac{1}{4}. If they make a profit of ₹ 3700 at the end of the year, let us write by calculating the profit share of Antony.

Solution:

Ratio of capitals of Samir, Idrish & Antony

= \frac{1}{6} : \frac{1}{5} : \frac{1}{4} = (\frac{1}{6} × 60) :(\frac{1}{5} × 60) :(\frac{1}{4} × 60) = 10 : 12 : 15

Total profit = ₹ 3700 \therefore Antony's share of profit = \frac{15}{10+12+15} × \text{ ₹ } 3700 = \frac{15}{37} × ₹ 3700 = ₹ 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

\therefore Ratio Capitals of Pritha, Rabeya & Jesmin = 8 : 12 : 15

Question 3

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.

Solution:

Total profit = ₹ 1500, Rajib's profit = ₹ 900

\therefore Aftab's profit = ₹ (1500-900) = ₹ 600

\therefore \frac{\text { Rajib's Capital }}{\text { Abtab's Capital }} = \frac{\text { Rajib's Profit. }}{\text { Abtab's Profit }}

\frac{\text { ₹ } 6000}{\text { Abtab's Capital }} = \frac{\text { ₹ } 900}{\text { ₹ } 600} = \frac{3}{2}

\therefore Aftab's Capital = \frac{2}{3} × ₹ 6000 = ₹ 4000.

Question 4

The ratio of capitals of three persons is 3 : 8 : 5, and the profit of 1st person is ₹ 60 less than of the 3rd person, let us calculate the total profit in this business.

Solution:

Ratio of capitals of 3 person = 3 : 8 : 5

\therefore Ratio of profit of 3 person = 3 : 8 : 5

Let profit of 1st person = ₹ 3x

Profit of 2nd person = ₹ 8x

Profit of 3rd person = ₹ 5x

Total profit = ₹ (3x + 8x + 5x) = ₹ 16x

Now, 5x - 3x = 60

or, 2x = 60 \thereforex = 30

Total profit = 16x = ₹ 16 × 30 = ₹ 480.

Question 5

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 shares. Let us calculate the amount of Jayanta's capital that was invested in the business.

Solution:

Ratio of profits of Jayanta, Ajit & Kunal

= ₹ 800 : ₹ 1000 : ₹ 1200 = 8 : 10 : 12 = 4 : 5 : 6

\therefore Ratio of their capitals = 4 : 5 : 6

Total capital = ₹ 15000

\therefore Jayanta's capital = \frac{4}{4+5+6} × \text{ ₹ } 15000 = \frac{4}{15} × ₹ 15000 = ₹ 4000.

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