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P, Q, R enter into a partnership. P initially invests 25 lakh & adds another 10 lakhs after one year. Q initially invests 35 lakh & withdrawal 10 lakh after 2 years and R invests Rs 30 Lakhs . In what ratio should the profit be divided at the end of 3 years?

Correct Answer: 19 : 19 : 18
P : Q : R
= (25 × 1 + 35 × 2) : (35 × 2 : 25 × 1) : (30 × 3)= 95 : 95 : 90= 19 : 19: 18

A, B and C enter into a partnership. A initially invests Rs. 25 lakhs and adds another Rs. 10 lakhs after one year. B initially invests Rs. 35 lakhs and withdraws Rs. 10 lakhs after 2 years and C invests Rs. 30 lakhs. In what ratio should the profits be divided at the end of 3 years ?

Consider the 5 × 5 matrix \[{\text{A}} = \left[ {\begin{array}{*{20}{c}} 1&2&3&4&5 \\ 5&1&2&3&4 \\ 4&5&1&2&3 \\ 3&4&5&1&2 \\ 2&3&4&5&1 \end{array}} \right

Jalal, Amit and Feroz enter into partnership. Jalal invests 4 times as much as Amit and Amit invests three-fourth of what Feroz invests. At the end of the financial year, the total profit earned is Rs. 19,000. Find the share for Jalal.

Alim and Badrul enter in to a partnership and Alim invests Tk 10,000 in the partnership. At the end of 4 months he withdraws Tk 2000. At the end of another 5 month, he withdraws another Tk 3000. If Badrul receives Tk 9600 as his share of the total profit of Tk 19,100 for the year, how much did Badrul invest in the company?

Let A be an m × n matrix and Ban n × m matrix. It is given that determinant ($$I$$m + AB) = determinant ($$I$$n + BA), where $$I$$k is the k × k identity matrix. Using the above property, the determinant of the matrix given below is
\[\left[ {\begin{array}{*{20}{c}} 2&1&1&1 \\ 1&2&1&1 \\ 1&1&2&1 \\ 1&1&1&2 \end{array}} \right

Eigen values of the matrix \[\left[ {\begin{array}{*{20}{c}} 0&1&0&0 \\ 1&0&0&0 \\ 0&0&0&{ - 2i} \\ 0&0&{2i}&0 \end{array}} \right

1. Withdrawal of prosecution can only be for all the accused persons in a case if there is more than one offence
2. Withdrawal of prosecution can be in respect of anyone or more of the offences
3. Withdrawal of prosecution has to be in respect of all the offences as it is the withdrawal of the case
Which of the following is correct?

Prakash, Sachin and Anil started a business jointly investing Rs. 11 lakh, Rs. 16.5 lakh and Rs.8.25 lakh respectively. The profit earned by them in the business at the end of 3 years was Rs. 19.5 lakh. What will be 50% of Anil's share in the profit ?

A, B and C are partners in a business partnership. A invested Rs. 4000 for whole year. B invested Rs. 6000 initially but increased this investment up to Rs. 8000 at the end of 4 months, while C invested Rs. 8000 initially, but withdraw Rs. 2000 at the end of 9 months. At the end of year total earned profit is Rs. 16950, find their share of profit ?

A , B and C enter into partnership by making investments in the ratio 3:5:7 . after a year , C invests another tk.337600 while a withdraws tk. 45600, the ratio of investments then changes to 24:59:87 . How much does a invest initially ?