Ganit Prakash - Class-X - Partnership Business
Let us work out 14 Arithmetic
📘 Let us work out 14 Solutions (Q1 - Q15)
Partnership BusinessGiven:
My capital = ₹ 15,000
Mala's capital = ₹ 25,000
Total profit = ₹ 16,800
First, we find the ratio of our capitals.
\[\begin{array}{l} \text{Ratio of capitals} = 15000 : 25000 \\ = 15 : 25 \\ = 3 : 5 \end{array}\]Sum of the ratio terms = \( 3 + 5 = 8 \)
Now, we divide the total profit according to the ratio of capitals.
\[\begin{array}{l} \text{My profit share} = \text{₹ } \left( 16800 \times \frac{3}{8} \right) \\ = \text{₹ } (2100 \times 3) \\ = \text{₹ } 6300 \end{array}\]\[\begin{array}{l} \text{Mala's profit share} = \text{₹ } \left( 16800 \times \frac{5}{8} \right) \\ = \text{₹ } (2100 \times 5) \\ = \text{₹ } 10500 \end{array}\]
Therefore, I will get ₹ 6,300 and Mala will get ₹ 10,500.
Given:
Priyam's capital = ₹ 15,000
Supriya's capital = ₹ 10,000
Bulu's capital = ₹ 25,000
Total loss = ₹ 3,000
First, we find the ratio of their capitals.
\[\begin{array}{l} \text{Ratio of capitals} = 15000 : 10000 : 25000 \\ = 15 : 10 : 25 \\ = 3 : 2 : 5 \quad \text{[Dividing by 5]} \end{array}\]Sum of the ratio terms = \( 3 + 2 + 5 = 10 \)
Now, we divide the total loss according to the ratio of their capitals.
\[\begin{array}{l} \text{Priyam must pay} = \text{₹ } \left( 3000 \times \frac{3}{10} \right) \\ = \text{₹ } (300 \times 3) \\ = \text{₹ } 900 \end{array}\]\[\begin{array}{l} \text{Supriya must pay} = \text{₹ } \left( 3000 \times \frac{2}{10} \right) \\ = \text{₹ } (300 \times 2) \\ = \text{₹ } 600 \end{array}\]
\[\begin{array}{l} \text{Bulu must pay} = \text{₹ } \left( 3000 \times \frac{5}{10} \right) \\ = \text{₹ } (300 \times 5) \\ = \text{₹ } 1500 \end{array}\]
Therefore, Priyam, Supriya, and Bulu must pay ₹ 900, ₹ 600, and ₹ 1,500 respectively to make up the loss.
Given:
Cost price of the car = ₹ 2,50,000
Selling price of the car = ₹ 2,62,500
Total profit = \( 262500 - 250000 = \text{₹ } 12,500 \)
Let Masud's capital be \( x \).
According to the problem, Sobha paid \( 1\frac{1}{2} \) times of Masud's capital.
Sobha's capital = \( 1\frac{1}{2} \times x = \frac{3}{2}x \)
Ratio of capitals of Sobha and Masud:
\[\begin{array}{l} = \frac{3}{2}x : x \\ = \frac{3}{2} : 1 \\ = 3 : 2 \end{array}\]Sum of the ratio terms = \( 3 + 2 = 5 \)
Now, we divide the total profit according to the ratio of capitals.
\[\begin{array}{l} \text{Sobha's profit share} = \text{₹ } \left( 12500 \times \frac{3}{5} \right) \\ = \text{₹ } (2500 \times 3) \\ = \text{₹ } 7500 \end{array}\]\[\begin{array}{l} \text{Masud's profit share} = \text{₹ } \left( 12500 \times \frac{2}{5} \right) \\ = \text{₹ } (2500 \times 2) \\ = \text{₹ } 5000 \end{array}\]
Therefore, Sobha's profit share is ₹ 7,500 and Masud's profit share is ₹ 5,000.
Given:
Capital of 1st friend = ₹ 5,000
Capital of 2nd friend = ₹ 6,000
Capital of 3rd friend = ₹ 7,000
Total loss = ₹ 1,800
First, we find the ratio of their capitals.
\[\begin{array}{l} \text{Ratio of capitals} = 5000 : 6000 : 7000 \\ = 5 : 6 : 7 \end{array}\]Sum of the ratio terms = \( 5 + 6 + 7 = 18 \)
Now, we calculate the amount each friend has to pay to make up the loss, according to the ratio of their capitals.
\[\begin{array}{l} \text{Amount 1st friend has to pay} = \text{₹ } \left( 1800 \times \frac{5}{18} \right) \\ = \text{₹ } (100 \times 5) \\ = \text{₹ } 500 \end{array}\]\[\begin{array}{l} \text{Amount 2nd friend has to pay} = \text{₹ } \left( 1800 \times \frac{6}{18} \right) \\ = \text{₹ } (100 \times 6) \\ = \text{₹ } 600 \end{array}\]
\[\begin{array}{l} \text{Amount 3rd friend has to pay} = \text{₹ } \left( 1800 \times \frac{7}{18} \right) \\ = \text{₹ } (100 \times 7) \\ = \text{₹ } 700 \end{array}\]
Therefore, the three friends have to pay ₹ 500, ₹ 600, and ₹ 700 respectively to make up the loss.
Given:
Capital of Dipu = ₹ 6,500
Capital of Rabeya = ₹ 5,200
Capital of Megha = ₹ 9,100
Total profit = ₹ 14,400
First, find the ratio of their capitals:
\[\begin{array}{l} \text{Ratio} = 6500 : 5200 : 9100 \\ = 65 : 52 : 91 \\ = 5 : 4 : 7 \quad \text{[Dividing by 13]} \end{array}\]Sum of ratio terms = \( 5 + 4 + 7 = 16 \)
According to the condition, \( \frac{2}{3} \)rd of the profit is divided equally.
\[\begin{array}{l} \frac{2}{3}\text{rd of profit} = \text{₹ } \left( 14400 \times \frac{2}{3} \right) \\ = \text{₹ } 9600 \end{array}\]Equally divided among 3 persons, each gets:
\[\begin{array}{l} = \text{₹ } \frac{9600}{3} = \text{₹ } 3200 \end{array}\]Remaining profit to be divided in capital ratio:
\[\begin{array}{l} = \text{₹ } (14400 - 9600) \\ = \text{₹ } 4800 \end{array}\]Share from remaining profit:
\[\begin{array}{l} \text{Dipu's share} = \text{₹ } \left( 4800 \times \frac{5}{16} \right) = \text{₹ } (300 \times 5) = \text{₹ } 1500 \\ \text{Rabeya's share} = \text{₹ } \left( 4800 \times \frac{4}{16} \right) = \text{₹ } (300 \times 4) = \text{₹ } 1200 \\ \text{Megha's share} = \text{₹ } \left( 4800 \times \frac{7}{16} \right) = \text{₹ } (300 \times 7) = \text{₹ } 2100 \end{array}\]Total Profit Share of Each:
\[\begin{array}{l} \text{Dipu's total share} = \text{₹ } (3200 + 1500) = \textbf{₹ 4,700} \\ \text{Rabeya's total share} = \text{₹ } (3200 + 1200) = \textbf{₹ 4,400} \\ \text{Megha's total share} = \text{₹ } (3200 + 2100) = \textbf{₹ 5,300} \end{array}\]Given:
Capital of 1st friend = ₹ 8,000
Capital of 2nd friend = ₹ 10,000
Capital of 3rd friend = ₹ 12,000
Total profit = ₹ 13,400
Bank instalment paid = ₹ 5,000
First, find the ratio of their capitals:
\[\begin{array}{l} \text{Ratio} = 8000 : 10000 : 12000 \\ = 8 : 10 : 12 \\ = 4 : 5 : 6 \quad \text{[Dividing by 2]} \end{array}\]Sum of ratio terms = \( 4 + 5 + 6 = 15 \)
Remaining profit after paying the bank instalment:
\[\begin{array}{l} = \text{₹ } (13400 - 5000) \\ = \text{₹ } 8400 \end{array}\]Now, we divide this remaining profit in the ratio of their capitals:
\[\begin{array}{l} \text{1st friend's profit share} = \text{₹ } \left( 8400 \times \frac{4}{15} \right) = \text{₹ } (560 \times 4) = \textbf{₹ 2,240} \\ \text{2nd friend's profit share} = \text{₹ } \left( 8400 \times \frac{5}{15} \right) = \text{₹ } (560 \times 5) = \textbf{₹ 2,800} \\ \text{3rd friend's profit share} = \text{₹ } \left( 8400 \times \frac{6}{15} \right) = \text{₹ } (560 \times 6) = \textbf{₹ 3,360} \end{array}\]Given:
Capital (loan) of 1st friend = ₹ 6,000
Capital (loan) of 2nd friend = ₹ 8,000
Capital (loan) of 3rd friend = ₹ 5,000
Total profit = ₹ 30,400
First, find the ratio of their capitals:
\[\begin{array}{l} \text{Ratio} = 6000 : 8000 : 5000 \\ = 6 : 8 : 5 \end{array}\]Sum of ratio terms = \( 6 + 8 + 5 = 19 \)
Profit shares before paying back the loan:
\[\begin{array}{l} \text{1st friend's share} = \text{₹ } \left( 30400 \times \frac{6}{19} \right) = \text{₹ } (1600 \times 6) = \text{₹ } 9600 \\ \text{2nd friend's share} = \text{₹ } \left( 30400 \times \frac{8}{19} \right) = \text{₹ } (1600 \times 8) = \text{₹ } 12800 \\ \text{3rd friend's share} = \text{₹ } \left( 30400 \times \frac{5}{19} \right) = \text{₹ } (1600 \times 5) = \text{₹ } 8000 \end{array}\]Individual share (remaining amount) after paying back the individual loan:
\[\begin{array}{l} \text{1st friend's individual share} = \text{₹ } (9600 - 6000) = \textbf{₹ 3,600} \\ \text{2nd friend's individual share} = \text{₹ } (12800 - 8000) = \textbf{₹ 4,800} \\ \text{3rd friend's individual share} = \text{₹ } (8000 - 5000) = \textbf{₹ 3,000} \end{array}\]Ratio of their shares:
\[\begin{array}{l} = 3600 : 4800 : 3000 \\ = 36 : 48 : 30 \\ = \textbf{6 : 8 : 5} \quad \text{[Dividing by 6]} \end{array}\]Given:
Capital of 1st friend (Driver) = ₹ 12,000
Capital of 2nd friend (Conductor 1) = ₹ 15,000
Capital of 3rd friend (Conductor 2) = ₹ 1,10,000
Total monthly profit = ₹ 29,260
First, find the ratio of their capitals:
\[\begin{array}{l} \text{Ratio} = 12000 : 15000 : 110000 \\ = 12 : 15 : 110 \end{array}\]Sum of capital ratio terms = \( 12 + 15 + 110 = 137 \)
According to the condition, \( \frac{2}{5} \)th of the profit is divided in the ratio 3:2:2.
\[\begin{array}{l} \frac{2}{5}\text{th of profit} = \text{₹ } \left( 29260 \times \frac{2}{5} \right) = \text{₹ } 11704 \end{array}\]Sum of work ratio terms = \( 3 + 2 + 2 = 7 \)
Shares from work allowance:
\[\begin{array}{l} \text{1st friend (Driver)} = \text{₹ } \left( 11704 \times \frac{3}{7} \right) = \text{₹ } (1672 \times 3) = \text{₹ } 5016 \\ \text{2nd friend (Conductor 1)} = \text{₹ } \left( 11704 \times \frac{2}{7} \right) = \text{₹ } (1672 \times 2) = \text{₹ } 3344 \\ \text{3rd friend (Conductor 2)} = \text{₹ } \left( 11704 \times \frac{2}{7} \right) = \text{₹ } (1672 \times 2) = \text{₹ } 3344 \end{array}\]Remaining profit to be divided in capital ratio:
\[\begin{array}{l} = \text{₹ } (29260 - 11704) = \text{₹ } 17556 \end{array}\]Shares from remaining profit:
\[\begin{array}{l} \text{1st friend} = \text{₹ } \left( 17556 \times \frac{12}{137} \right) = \text{₹ } (128 \times 12) = \text{₹ } 1536 \\ \text{2nd friend} = \text{₹ } \left( 17556 \times \frac{15}{137} \right) = \text{₹ } (128 \times 15) = \text{₹ } 1920 \\ \text{3rd friend} = \text{₹ } \left( 17556 \times \frac{110}{137} \right) = \text{₹ } (128 \times 110) = \text{₹ } 14080 \end{array}\]Total Share of Each:
\[\begin{array}{l} \text{1st friend's total share} = \text{₹ } (5016 + 1536) = \textbf{₹ 6,552} \\ \text{2nd friend's total share} = \text{₹ } (3344 + 1920) = \textbf{₹ 5,264} \\ \text{3rd friend's total share} = \text{₹ } (3344 + 14080) = \textbf{₹ 17,424} \end{array}\]Explanation:
In a partnership business where capitals change during the year, we calculate the equivalent capital for 1 month for each partner.
Pradipbabu's equivalent capital for 1 month:
He invested ₹ 24,000 for the first 5 months.
After 5 months, he invested ₹ 4,000 more, making his capital ₹ (24,000 + 4,000) = ₹ 28,000 for the remaining (12 - 5) = 7 months.
Aminabibi's equivalent capital for 1 month:
She invested ₹ 30,000 for the entire 12 months.
Ratio of their equivalent capitals:
\[\begin{array}{l} = 316000 : 360000 \\ = 316 : 360 \\ = 79 : 90 \quad \text{[Dividing by 4]} \end{array}\]Sum of ratio terms = \( 79 + 90 = 169 \)
Total yearly profit = ₹ 27,716
Profit shares:
\[\begin{array}{l} \text{Pradipbabu's share} = \text{₹ } \left( 27716 \times \frac{79}{169} \right) = \text{₹ } (164 \times 79) = \textbf{₹ 12,956} \\ \text{Aminabibi's share} = \text{₹ } \left( 27716 \times \frac{90}{169} \right) = \text{₹ } (164 \times 90) = \textbf{₹ 14,760} \end{array}\]Explanation:
We calculate the equivalent capital for 1 month for each partner based on how long each amount was invested.
Niyamat chacha's equivalent capital for 1 month:
He invested ₹ 30,000 for 6 months.
Then he added ₹ 40,000, so his capital became ₹ 70,000 for the remaining 6 months.
Karabi didi's equivalent capital for 1 month:
She invested ₹ 50,000 for 6 months.
Then she withdrew ₹ 10,000, so her capital became ₹ 40,000 for the remaining 6 months.
Ratio of their equivalent capitals:
\[\begin{array}{l} = 600000 : 540000 \\ = 60 : 54 \\ = 10 : 9 \quad \text{[Dividing by 6]} \end{array}\]Sum of ratio terms = \( 10 + 9 = 19 \)
Total yearly profit = ₹ 19,000
Profit shares:
\[\begin{array}{l} \text{Niyamat chacha's share} = \text{₹ } \left( 19000 \times \frac{10}{19} \right) = \text{₹ } (1000 \times 10) = \textbf{₹ 10,000} \\ \text{Karabi didi's share} = \text{₹ } \left( 19000 \times \frac{9}{19} \right) = \text{₹ } (1000 \times 9) = \textbf{₹ 9,000} \end{array}\]Explanation:
Initial capital ratio of Srikant and Soiffuddin:
\[\begin{array}{l} = 240000 : 300000 \\ = 24 : 30 \\ = 4 : 5 \end{array}\]When Peter joins with ₹ 81,000, Srikant and Soiffuddin withdraw this amount in the ratio 4:5.
Amount withdrawn by Srikant = \( 81000 \times \frac{4}{9} = \text{₹ } 36,000 \)
Amount withdrawn by Soiffuddin = \( 81000 \times \frac{5}{9} = \text{₹ } 45,000 \)
Now, calculate equivalent capital for 1 month for each:
Srikant's equivalent capital:
₹ 2,40,000 for 4 months, then ₹ (2,40,000 - 36,000) = ₹ 2,04,000 for 8 months.
Soiffuddin's equivalent capital:
₹ 3,00,000 for 4 months, then ₹ (3,00,000 - 45,000) = ₹ 2,55,000 for 8 months.
Peter's equivalent capital:
He joined after 4 months, so his ₹ 81,000 was invested for 8 months.
Ratio of their effective capitals (Srikant : Soiffuddin : Peter):
\[\begin{array}{l} = 2592000 : 3240000 : 648000 \\ = 2592 : 3240 : 648 \quad \text{[Dividing by 1000]} \\ = 324 : 405 : 81 \quad \text{[Dividing by 8]} \\ = 4 : 5 : 1 \quad \text{[Dividing by 81]} \end{array}\]Sum of ratio terms = \( 4 + 5 + 1 = 10 \)
Total profit = ₹ 39,150
Profit shares:
\[\begin{array}{l} \text{Srikant's share} = \text{₹ } \left( 39150 \times \frac{4}{10} \right) = \text{₹ } (3915 \times 4) = \textbf{₹ 15,660} \\ \text{Soiffuddin's share} = \text{₹ } \left( 39150 \times \frac{5}{10} \right) = \text{₹ } (3915 \times 5) = \textbf{₹ 19,575} \\ \text{Peter's share} = \text{₹ } \left( 39150 \times \frac{1}{10} \right) = \text{₹ } (3915 \times 1) = \textbf{₹ 3,915} \end{array}\]Explanation:
Let Arun invest the additional ₹ 12,000 after \( x \) months.
Arun's equivalent capital for 1 month:
He invested ₹ 24,000 for the first \( x \) months, and then ₹ (24,000 + 12,000) = ₹ 36,000 for the remaining \( (12 - x) \) months.
Ajoy's equivalent capital for 1 month:
He invested ₹ 30,000 for the entire 12 months.
Ratio of their effective capitals (Arun : Ajoy):
\[\begin{array}{l} = (432000 - 12000x) : 360000 \\ = 12000(36 - x) : 360000 \\ = (36 - x) : 30 \quad \text{[Dividing by 12000]} \end{array}\]Sum of the ratio terms = \( (36 - x) + 30 = 66 - x \)
Total profit = ₹ 14,030 and Arun's profit share = ₹ 7,130.
According to the problem, Arun's share from the total profit is:
\[\begin{array}{l} 14030 \times \frac{36 - x}{66 - x} = 7130 \\ \Rightarrow \frac{36 - x}{66 - x} = \frac{7130}{14030} \\ \Rightarrow \frac{36 - x}{66 - x} = \frac{713}{1403} \end{array}\]Dividing numerator and denominator of the RHS by 23:
\[\begin{array}{l} \Rightarrow \frac{36 - x}{66 - x} = \frac{31}{61} \\ \Rightarrow 61(36 - x) = 31(66 - x) \\ \Rightarrow 2196 - 61x = 2046 - 31x \\ \Rightarrow 2196 - 2046 = 61x - 31x \\ \Rightarrow 150 = 30x \\ \Rightarrow x = 5 \end{array}\]Therefore, Arun invested the additional money after 5 months.
Explanation:
Total profit made = ₹ 1,39,100
Annual bank instalment paid = ₹ 28,100
Remaining profit = \( 139100 - 28100 = \text{₹ } 1,11,000 \)
According to the contract, this remaining profit is divided into two halves.
Half of the remaining profit = \( \frac{111000}{2} = \text{₹ } 55,500 \)
Part 1: Divided Equally
The first half (₹ 55,500) is divided equally among the 3 modellers.
\[\begin{array}{l} \text{Each gets} = \text{₹ } \frac{55500}{3} = \text{₹ } 18,500 \end{array}\]Part 2: Divided by Working Days
The other half (₹ 55,500) is divided in the ratio of their working days: 300 : 275 : 350.
\[\begin{array}{l} \text{Ratio} = 300 : 275 : 350 \\ = 12 : 11 : 14 \quad \text{[Dividing by 25]} \end{array}\]Sum of ratio terms = \( 12 + 11 + 14 = 37 \)
Shares from this part:
\[\begin{array}{l} \text{1st modeller} = \text{₹ } \left( 55500 \times \frac{12}{37} \right) = \text{₹ } (1500 \times 12) = \text{₹ } 18,000 \\ \text{2nd modeller} = \text{₹ } \left( 55500 \times \frac{11}{37} \right) = \text{₹ } (1500 \times 11) = \text{₹ } 16,500 \\ \text{3rd modeller} = \text{₹ } \left( 55500 \times \frac{14}{37} \right) = \text{₹ } (1500 \times 14) = \text{₹ } 21,000 \end{array}\]Total Share of Each Modeller:
\[\begin{array}{l} \text{1st modeller's total share} = \text{₹ } (18500 + 18000) = \textbf{₹ 36,500} \\ \text{2nd modeller's total share} = \text{₹ } (18500 + 16500) = \textbf{₹ 35,000} \\ \text{3rd modeller's total share} = \text{₹ } (18500 + 21000) = \textbf{₹ 39,500} \end{array}\]Explanation:
Let the total profit be ₹ \( x \).
Ratio of their capitals = 40000 : 50000 = 4 : 5. (Sum of ratio terms = 9)
Part 1: 50% divided equally
50% of profit = \( \frac{x}{2} \). Since it is divided equally, each friend gets \( \frac{x}{4} \).
Part 2: Remaining 50% divided by capital ratio
The remaining profit is also \( \frac{x}{2} \).
\[\begin{array}{l} \text{1st friend gets} = \frac{x}{2} \times \frac{4}{9} = \frac{4x}{18} = \frac{2x}{9} \\ \text{2nd friend gets} = \frac{x}{2} \times \frac{5}{9} = \frac{5x}{18} \end{array}\]Total Share of Each:
\[\begin{array}{l} \text{1st friend's total share} = \frac{x}{4} + \frac{2x}{9} \\ \text{2nd friend's total share} = \frac{x}{4} + \frac{5x}{18} \end{array}\]Given that the 1st friend's profit is ₹ 800 less than the 2nd friend's profit:
\[\begin{array}{l} \left(\frac{x}{4} + \frac{5x}{18}\right) - \left(\frac{x}{4} + \frac{2x}{9}\right) = 800 \\ \Rightarrow \frac{5x}{18} - \frac{2x}{9} = 800 \\ \Rightarrow \frac{5x - 4x}{18} = 800 \\ \Rightarrow \frac{x}{18} = 800 \\ \Rightarrow x = 800 \times 18 = 14400 \end{array}\]The total profit is ₹ 14,400.
Now, substitute \( x = 14400 \) to find the 1st friend's share:
\[\begin{array}{l} = \frac{14400}{4} + \frac{2(14400)}{9} \\ = 3600 + 2(1600) \\ = 3600 + 3200 = 6800 \end{array}\]Therefore, the share of profit of the first friend is ₹ 6,800.
(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.
Note: Based on the original Bengali context of this problem, the allowance for keeping accounts in condition (ii) is considered a monthly allowance. We will solve it accordingly.
Explanation:
Total profit at the end of the year = ₹ 6,960.
Deductions from the profit:
1. Yearly business expense = \( 125 \times 12 = \text{₹ } 1,500 \)
2. Account keeping allowance for Puja = \( 200 \times 12 = \text{₹ } 2,400 \)
3. Account keeping allowance for Uttam = \( 200 \times 12 = \text{₹ } 2,400 \)
\[\begin{array}{l} \text{Total deductions} = 1500 + 2400 + 2400 = \text{₹ } 6,300 \end{array}\]Distributable Profit:
\[\begin{array}{l} \text{Remaining profit} = 6960 - 6300 = \text{₹ } 660 \end{array}\]This remaining ₹ 660 is divided in the ratio of their capitals.
\[\begin{array}{l} \text{Ratio} = 5000 : 7000 : 10000 \\ = 5 : 7 : 10 \end{array}\]Sum of ratio terms = \( 5 + 7 + 10 = 22 \)
Shares from the distributable profit:
\[\begin{array}{l} \text{Puja's share} = \text{₹ } \left( 660 \times \frac{5}{22} \right) = \text{₹ } (30 \times 5) = \text{₹ } 150 \\ \text{Uttam's share} = \text{₹ } \left( 660 \times \frac{7}{22} \right) = \text{₹ } (30 \times 7) = \text{₹ } 210 \\ \text{Meher's share} = \text{₹ } \left( 660 \times \frac{10}{22} \right) = \text{₹ } (30 \times 10) = \text{₹ } 300 \end{array}\]Total Share of Each:
\[\begin{array}{l} \text{Puja's total share} = (\text{Allowance} + \text{Profit}) = 2400 + 150 = \textbf{₹ 2,550} \\ \text{Uttam's total share} = (\text{Allowance} + \text{Profit}) = 2400 + 210 = \textbf{₹ 2,610} \\ \text{Meher's total share} = (\text{Profit only}) = \textbf{₹ 300} \end{array}\]📘 16. Very short Answer : (V.S.A.)
(A) M.C.Q.Explanation:
The ratio of their profit share will be equal to the ratio of their capitals (since the time period is the same for all).
\[\begin{array}{l} \text{Ratio of profit} = 200 : 150 : 250 \\ = 20 : 15 : 25 \quad \text{[Dividing by 10]} \\ = 4 : 3 : 5 \quad \text{[Dividing by 5]} \end{array}\]Correct Option: (b) 4:3:5
Explanation:
Ratio of capitals of Suvendu and Nousad:
\[\begin{array}{l} = 1500 : 1000 \\ = 15 : 10 \\ = 3 : 2 \end{array}\]Sum of ratio terms = \( 3 + 2 = 5 \)
Total loss = ₹ 75
Suvendu's share of the loss:
\[\begin{array}{l} = \text{₹ } \left( 75 \times \frac{3}{5} \right) \\ = \text{₹ } (15 \times 3) \\ = \text{₹ } 45 \end{array}\]Correct Option: (a) ₹ 45
Explanation:
The ratio of their investments is equal to the ratio of their profit shares.
\[\begin{array}{l} \text{Ratio of profit} = 50 : 100 : 150 \\ = 1 : 2 : 3 \end{array}\]Sum of ratio terms = \( 1 + 2 + 3 = 6 \)
Total investment = ₹ 6000
Smita's investment:
\[\begin{array}{l} = \text{₹ } \left( 6000 \times \frac{3}{6} \right) \\ = \text{₹ } \left( 6000 \times \frac{1}{2} \right) \\ = \text{₹ } 3000 \end{array}\]Correct Option: (c) ₹ 3000
Explanation:
Total profit = ₹ 69
Bimal's profit = ₹ 46
Amal's profit = ₹ (69 - 46) = ₹ 23
Profit Ratio (Amal : Bimal) = \( 23 : 46 = 1 : 2 \)
Let Bimal's capital be ₹ \( x \).
Amal's effective capital = ₹ \( 500 \times 9 = 4500 \)
Bimal's effective capital = ₹ \( x \times 6 = 6x \)
Since the ratio of effective capitals equals the ratio of profit:
\[\begin{array}{l} \frac{4500}{6x} = \frac{1}{2} \\ \Rightarrow 6x = 4500 \times 2 \\ \Rightarrow 6x = 9000 \\ \Rightarrow x = 1500 \end{array}\]Bimal's capital is ₹ 1500.
Correct Option: (a) ₹ 1500
Explanation:
The ratio of their profit shares will be equal to the ratio of their effective capitals.
Pallabi's effective capital = ₹ \( 500 \times 9 = 4500 \)
Rajiya's effective capital = ₹ \( 600 \times 5 = 3000 \)
\[\begin{array}{l} \text{Profit Ratio (Pallabi : Rajiya)} = 4500 : 3000 \\ = 45 : 30 \\ = 3 : 2 \quad \text{[Dividing by 15]} \end{array}\]Correct Option: (a) 3:2
📘 16. Very short Answer : (V.S.A.)
(B) True or FalseAt least 3 persons are needed in partnership business.
Explanation:
A partnership business requires a minimum of 2 persons to start and operate. It is not mandatory to have 3 persons.
Answer: False
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.
Explanation:
The ratio of profit share is equal to the ratio of their capitals.
Profit Ratio (Raju : Ashif) = 5 : 4
Given Raju's profit share = ₹ 80.
\[\begin{array}{l} \text{Let Ashif's profit share be } x. \\ \frac{5}{4} = \frac{80}{x} \\ \Rightarrow 5x = 320 \\ \Rightarrow x = 64 \end{array}\]So, Ashif should get ₹ 64, not ₹ 100.
Answer: False
📘 16. Very short Answer : (V.S.A.)
(C) Fill in the blanksExplanation:
Based on the time of investment, partnership business is generally classified into two types: Simple Partnership and Compound Partnership.
Answer: two (2)
Explanation:
When the capital of all partners is invested for the same duration of time, the profit or loss is distributed purely in the ratio of their invested capitals. This is known as a simple partnership.
Answer: simple
Explanation:
When the capitals are invested for varying time periods, the profit or loss is distributed based on the ratio of the product of capital and respective time periods (equivalent capital). This is known as a compound partnership.
Answer: compound
📘 17. Short answer type question : (S.A.)
Partnership BusinessExplanation:
First, we convert the fractional ratio of capitals into a whole number ratio by multiplying with the LCM of the denominators (6, 5, 4).
LCM of 6, 5, and 4 is 60.
\[\begin{array}{l} \text{Ratio of capitals} = \frac{1}{6} : \frac{1}{5} : \frac{1}{4} \\ = \left(\frac{1}{6} \times 60\right) : \left(\frac{1}{5} \times 60\right) : \left(\frac{1}{4} \times 60\right) \\ = 10 : 12 : 15 \end{array}\]Sum of ratio terms = \( 10 + 12 + 15 = 37 \)
Total profit = ₹ 3,700
Since the time periods are the same, the profit is distributed in the ratio of their capitals.
\[\begin{array}{l} \text{Antony's profit share} = \text{₹ } \left( 3700 \times \frac{15}{37} \right) \\ = \text{₹ } (100 \times 15) \\ = \text{₹ } 1500 \end{array}\]Therefore, the profit share of Antony is ₹ 1,500.
Explanation:
Given ratios:
\[\begin{array}{l} \text{Pritha} : \text{Rabeya} = 2 : 3 \\ \text{Rabeya} : \text{Jesmin} = 4 : 5 \end{array}\]To find the combined ratio, we need to make the value corresponding to "Rabeya" the same in both ratios. The LCM of 3 and 4 is 12.
Multiply the first ratio by 4:
\[\begin{array}{l} \text{Pritha} : \text{Rabeya} = (2 \times 4) : (3 \times 4) = 8 : 12 \end{array}\]Multiply the second ratio by 3:
\[\begin{array}{l} \text{Rabeya} : \text{Jesmin} = (4 \times 3) : (5 \times 3) = 12 : 15 \end{array}\]Now that Rabeya's part is 12 in both, we can combine them.
\[\begin{array}{l} \text{Pritha} : \text{Rabeya} : \text{Jesmin} = 8 : 12 : 15 \end{array}\]Therefore, the ratio of capitals of Pritha, Rabeya, and Jesmin is 8 : 12 : 15.
Explanation:
Total profit = ₹ 1,500
Rajib's profit = ₹ 900
Abtab's profit = ₹ (1500 - 900) = ₹ 600
In a simple partnership, the ratio of capitals is equal to the ratio of profits.
\[\begin{array}{l} \text{Ratio of profits (Rajib : Abtab)} = 900 : 600 \\ = 9 : 6 \\ = 3 : 2 \end{array}\]Let the capital of Abtab be ₹ \( x \).
\[\begin{array}{l} \text{Ratio of capitals (Rajib : Abtab)} = 6000 : x \end{array}\]Equating the two ratios:
\[\begin{array}{l} \frac{6000}{x} = \frac{3}{2} \\ \Rightarrow 3x = 6000 \times 2 \\ \Rightarrow 3x = 12000 \\ \Rightarrow x = 4000 \end{array}\]Therefore, the capital of Abtab was ₹ 4,000.
Explanation:
The ratio of their profits is the same as the ratio of their capitals, which is 3 : 8 : 5.
Let their respective profits be ₹ \( 3x \), ₹ \( 8x \), and ₹ \( 5x \).
Total profit = \( 3x + 8x + 5x = 16x \).
According to the problem, the profit of the 1st person is ₹ 60 less than the profit of the 3rd person.
\[\begin{array}{l} \text{3rd person's profit} - \text{1st person's profit} = 60 \\ \Rightarrow 5x - 3x = 60 \\ \Rightarrow 2x = 60 \\ \Rightarrow x = 30 \end{array}\]Now, we can find the total profit:
\[\begin{array}{l} \text{Total profit} = 16x \\ = 16 \times 30 \\ = 480 \end{array}\]Therefore, the total profit in this business is ₹ 480.
Explanation:
Total capital invested = ₹ 15,000
The ratio of their capitals is equal to the ratio of their profit shares.
\[\begin{array}{l} \text{Ratio of profits (Jayanta : Ajit : Kunal)} = 800 : 1000 : 1200 \\ = 8 : 10 : 12 \quad \text{[Dividing by 100]} \\ = 4 : 5 : 6 \quad \text{[Dividing by 2]} \end{array}\]So, the ratio of their capitals is 4 : 5 : 6.
Sum of the ratio terms = \( 4 + 5 + 6 = 15 \)
To find Jayanta's capital, we use his proportion in the total capital.
\[\begin{array}{l} \text{Jayanta's capital} = \text{Total Capital} \times \frac{4}{15} \\ = 15000 \times \frac{4}{15} \\ = 1000 \times 4 \\ = 4000 \end{array}\]Therefore, the amount of Jayanta's capital invested in the business was ₹ 4,000.
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