## Partnership Questions - 1

Hari and Giri started a business by investing Rs.45000 and Rs.54000 respectively. What is the share of Giri out of annual profit of Rs.13200 ?
• Rs.6000
• Rs.5400
• Rs.6200
• Rs.7200
• Rs.8200
Explanation

Investment Ratio = Profit Sharing Ratio.

Ratio of Investments Hari : Giri = Rs.45000 : 54000 => 5 : 6.

Giri share = $\displaystyle 13200 \times \frac{6}{11}$ = Rs.7200

Hari share = $\displaystyle 13200 \times \frac{5}{11}$ = Rs.6000

Workspace
Kumar and Amarâ€™s investments in a business are in the ratio 8 : 9 and their annual profit is Rs.20400, which is 12.5% of their investments, then investment of Kumar is ?
• Rs.86000
• Rs.96000
• Rs.96400
• Rs.86000
• Rs.76800
Explanation

As profit is 12.5% of the investment

Total investment = $\displaystyle \frac{20400}{12.5} \times 100$ = 163200.

Investment of Kumar = 163200 $\displaystyle \times \frac{8}{17}$ = Rs.76800.

Investment of Amar = 163200 $\displaystyle \times \frac{9}{17}$ = Rs.86400.

Workspace
X and Y started a business by investing Rs.36000 and Rs.42000 respectively after 4 months Z joined in the business with an investment of Rs.48000, then find share of Z in the profit of Rs.13750 ?
• Rs.3200
• Rs.4000
• Rs.3250
• Rs.3825
• Rs.3985
Explanation

Ratio of investment, as investments is for different time.

Investment x Number of units of time.

Ratio of investments X : Y : Z = 36000 : 42000 : 48000 => 6 : 7 : 8.

X = 6 x 12 Months = 72, Y = 7 x 12 = 84, Z = 8 X 8 = 64 => 18 : 21 : 16.

Ratio of investments => X : Y : Z = 18 : 21 : 16.

Investment Ratio = Profit sharing Ratio.

Z = $\displaystyle 13750 \times \frac{16}{55}$ = Rs.4000.

Share of Z in the profit is Rs.4000.

Workspace
Kala and Sudha stated a business with an investment of Rs.18000 and Rs.24000 respectively. After 3 months Gita joined in the business with an investment of Rs.20000, find share of Gita, if the difference between the profits received by Kala and Sudha is Rs.840 ?
• Rs.2150
• Rs.2200
• Rs.2100
• Rs.2250
• Rs.2300
Explanation

Ratio of investments Kala : Sudha : Githa => 18000 : 24000 : 20000 => 9 : 12 : 10.

Investment x time.

Kala = 9 x 12 = 108.

Sudha = 12 x 12 = 144.

Githa = 10 x 9 = 180.

Or Kala : Sudha : Githa => 6 : 8 : 5.

Let shares of Kala, Sudha and Githa be = 6a : 8a : 5a.

Difference between the profits received by Kala and Sudha

6a â€“ 8a = 2a = 840 or a = 420.

Githa = 5a = 5 x 420 = Rs.2100.

Workspace
In a business A invested 10% more amount than B, B invested 20% more amount than C, what is share of B in a profit of Rs.36960 ?
• Rs.12000
• Rs.11500
• Rs.11800
• Rs.12600
• Rs.12800
Explanation

Let share of C be Rs.100, then B = C + 20% = 100 + 100 $\displaystyle \times \frac{20}{100}$ = Rs.120.

A = B + 10% => 120 + 120 $\displaystyle \times \frac{10}{100}$ = Rs.132.

Ratio of investments = A : B : C = 132 : 120 : 100 => 33 : 30 : 25.

B share in the profit = 36960 $\displaystyle \times \frac{30}{88}$ = Rs.12600.

Workspace
In a business X invested 20% more than Y and 30% more than Z. Difference between the shares in the profit received by X and Z is Rs.4140. then total profit in the business is ?
• Rs.42000
• Rs.46690
• Rs.42400
• Rs.44400
• Rs.43280
Explanation

Let Z investment be 100, then X = 130.

Let Y investment be 100, then X = 120.

Z : X1 : : X2 : Y = 100 : 130 : : 120 : 100 => 10 : 13 : : 12 : 10.

Z = Z x X2 = 10 x 12 = 120.

X = X1 x X2 = 13 x 12 = 156.

Y = X1 x Y = 13 x 10 = 130.

Therefore X : Y : Z = 156 : 130 : 120 or 78 : 65 : 60 = sum of units = 203.

Difference between X and Z = 78 â€“ 60 => 18 units.

Total profit = $\displaystyle \frac{4140}{18} \times 203$ = Rs.46690.

Workspace
Kant and Jaya started a business by investing a certain amount, Jayaâ€™s share is Rs.1400, out of annual profit of Rs.3800, then what is the ratio of investments of Kant and Jaya respectively ?
• 3 : 4
• 18 : 21
• 12 : 7
• 6 : 11
• 4 : 3
Explanation

Total profit = Rs.3800.

Jaya share = Rs.1400.

Kant share = Rs.3800 - Rs.1400 = Rs.2400.

Kant : Jaya = 2400 : 1400 => 12 : 7

Workspace
Giri started a business with an investment of Rs.30000. after some months Suri joined in the business with an investment of Rs.32000 as his share. Suri received Rs.720 out of annual profit of Rs.1800. after how many months did Suri join in the business ?
• 3 months
• 4 months
• 3 $\displaystyle \frac{1}{2}$ months
• 4 $\displaystyle \frac{1}{2}$ months
• 2 months
Explanation

Total profit = Rs.1800.

Suri share in the profit = Rs.720.

Giri share in the profit = Rs.1800 â€“ Rs.720 = Rs.1080.

Ratio of shares = Giri : Suri = 1080 : 720 = 3 : 2.

Ratio of investments as investments is for different time

Investment x Time

Giri = Rs.30000 x 12 = Rs.360000.

Let Suri in the business for â€˜aâ€™ months.

Suri = Rs.32000 x a = Rs.32000a.

Rs.32000a = $\displaystyle \frac{360000}{3} \times 2$ = Rs.240000.

Suri = investment x Time = Rs.240000.

Time â€˜aâ€™ = $\displaystyle \frac{240000}{32000}$ = = 7.5 or 7 $\displaystyle \frac{1}{2}$ months.

Therefore Suri joined after 12 â€“ 7 $\displaystyle \frac{1}{2} = 4 \frac{1}{2}$ months.

Workspace
Manu and Sunanda started a business by investing Rs.150000 and Rs.175000, Manu is also a working partner. Both Manu and Sunanda received equal amount in the annual profit of Rs.16800 which includes salary of Manu, find salary of Manu ?
• Rs.1800
• Rs.900
• Rs.1200
• Rs.2400
• Rs.1080
Explanation

Ratio of shares Manu : Sunanda = 150000 : 175000 => 30 : 35 => 6 : 7.

Manu and Sunanda received equal profit then profit of each partner is $\displaystyle \frac{16800}{2}$ = Rs.8400.

Sunanda = Rs.8400, Manu = Profit + salary = Rs.8400.

Share of Manu excluding salary = $\displaystyle \frac{8400}{7} \times 6$ = Rs.7200.

Salary of Manu = Rs.8400 â€“ Rs.7200 = Rs.1200.

Workspace
Mukesh and Suresh started a business by investing Rs.40000 and Rs.50000 respectively. After 4 months Suresh has withdrawn Rs.5000 from the business. Find share of Suresh in the annual profit of Rs.8450 ?
• Rs.3950
• Rs.4550
• Rs.4650
• Rs.5200
• Rs.5150
Explanation

Mukesh = 40000 x 12 = 480000.

Suresh = 50000 x 4 = 200000.

45000 x 8 = 360000 = 560000.

Ratio Mukesh : Suresh = 480000 : 560000 = 6 : 7.

Suresh = $\displaystyle 8450 \times \frac{7}{13}$ = Rs.4550.

Mukesh = $\displaystyle 8450 \times \frac{6}{13}$ = Rs.3900.

Workspace

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