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Arithmetic: Partnership Test-2

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Question 1
A, B and C enter into a partnership. A invests some money at the beginning ,B invests double the amount after 6 months and C invests thrice the amount after 8 months. If the annual profit be Rs.27000 C’s share is:
A
Rs.9000
B
Rs.11250
C
Rs.10,800
D
Rs.8625
Question 1 Explanation: 
Ratio of profit
$ \displaystyle \begin{array}{l}=x\times 12:2x\times 6:3x\times 4\\=1:1:1\\\therefore \,\,\,C's\,\,\,share=\frac{1}{3}\times 27000\\=Rs.\,9000\end{array}$
Question 2
X, Y and Z were sharing profits in the ratio 4: 3: 2. Y retired from the firm and X and Z decide to share profits in the ratio 3: 2. Calculate the gaining ratio.
A
7: 8
B
5: 9
C
4: 7
D
5: 8
Question 2 Explanation: 
Gaining ratio
$ \displaystyle \begin{array}{l}=\left( \frac{3}{5}-\frac{4}{9} \right):\left( \frac{2}{5}-\frac{2}{9} \right)\\=\frac{27-20}{45}:\frac{18-10}{45}=7:8\end{array}$
Question 3
Karan starts a business by investing Rs.60000. six months later Shirish joins him by investing Rs.100000. At the end of one year from commencement of the business, they earn a profit of Rs.151800. What is the Shirish’s share in the profit?
A
Rs.55200
B
Rs.82800
C
Rs.62500
D
none
Question 3 Explanation: 
Ratio of the Profit = Ratio of the equivalent capitals of Karan and Shirish for 1 month
$ \displaystyle \begin{array}{l}=60000\times 12:100000\times 6\\=720000:600000=6:5\\\therefore \,\,\,Shirish's\,\,\,share\,\,\,in\,\,the\,\,\,profit\\=Rs.\,\left( \frac{5}{11}\times 151800 \right)=Rs.69000\end{array}$
Question 4
Prakash, Sunil and Anil started a business jointly investing Rs.11 lakhs , Rs. 16.5 lakh and Rs. 8.25 lakhs respectively. The profit earned by them in the business at the end of three years was Rs.19.5 lakhs. What will be the 50% of Anil’s share in the profit?
A
Rs.4.5 lakhs
B
Rs.2.25 lakhs
C
Rs.2.5 lakhs
D
Rs.3.75 lakhs
Question 4 Explanation: 
Ratio of the equivalent capitals of Prakash, Sunil and Anil for 1 month
= 11 X 36: 16.5 X 36 : 8.25 X 36
= 4:6:3
Therefore Anil’s share in the profit
{3/(4+6+3)} X 19.5
= 4.5 lakh
Therefore 50% of 4.5
2.25 lakh
Question 5
Sonu invested 10% more than Mona. Mona invested 10% less than Raghu. If the total sum of their investment is Rs.5780, how much amount did Raghu invest?
A
Rs.2010
B
Rs.2000
C
Rs.2100
D
Rs.2210
Question 5 Explanation: 
Let Mona’s investment=Rs.100
Therefore Sonu’s investment = Rs.110
And Raghu’s investment
$ \displaystyle =Rs.\,\frac{1000}{9}$
Therefore Ratio of Mona’s, Sonu’s and Raghu’s investments
$ \displaystyle =100:110:\frac{1000}{9}=90:99:100$
Sum of ratios = 90 + 99 + 100 = 289
Therefore Raghu’s investment
$ \displaystyle =Rs.\,\left( \frac{100}{289}\times 5780 \right)=Rs.2000$
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