Saturday, 14 February 2015

02. Aptitude Questions with Solutions ---- PARTNERSHIPS Solved Problems



   Aptitude  Partnerships  Solved Problem 1  
 . A , B and C invested Rs 18000 , Rs 24000 and Rs.36000 in a business respectively. What is the ratio of shares of their profits ?
   a) 3 : 4 :5               b) 2 : 3 :6             c) 3 : 4 : 6            d) 2 : 5 :7 b   e) 3 : 5 : 8
   Answer : C
   Explanation:
       Ratio of Profits = Ratio of the sums invested
                            = 18000:  24000 :  36000
                            = 3 :  4 :  6

    Aptitude Partnerships  Solved Problem 2 
    A and B enter into partnership. A invests Rs 16000 and B invests Rs 20000. If the profit at the end of the year amounts to Rs  27000. what would be the share of B in the profit ?
     a) Rs 10000            b) Rs 110000          c)Rs 12000            d)Rs 15000      e)Rs 21000
    Answer : D
    Explanation:

            The ratio of the investment of capitals of A and B is 16000 : 20000 = 4 : 5

               So they have to share the profit in the ratio of 4 : 5

           B's share of profit =  $ \frac{5}{9}$ X 27000 = 15000

    Aptitude Partnerships  Solved Problem 3  
     A and B Started a business by investing Rs. 90000 and Rs. 165000 respectively. Find the share of A, out of an annual profit of Rs.85000
     a) Rs 30000          b)Rs 35000         c)Rs 55000         d)Rs 60000        e) Rs 62000
    Answer : A
    Explanation:
    Ratio of their shares in the profit = 90000: 165000 
                                                         = 6: 11
           :. A' s share = Rs.$ [85000 \times \frac{6}{17} ] $  ]= Rs. 30000 

    Aptitude  Partnerships  Solved Problem 4                              
     A, B and C invested Rs 40000, Rs 100000 and Rs 80000 respectively in a business. The net proift for the years was Rs 24200 which was divided in proportion to their investments. Find the amount of profit B earned ?
     a)  Rs 8800            b) Rs 2200          c) Rs 5500         d)Rs 6000      e)Rs 7500
   Answer : A
   Explanation :                   Ratio of profits = Ratio of the capitals

                                             =   40000 : 100000 :  80000
                                             =  2 : 5 : 4
            Share of C in the annual profit Rs 24200 = 24200 X $\frac{4}{11} $   =   Rs 8800 
    
    Aptitude  Partnerships  Solved Problem 5 
    A,B and C invested their capitals in the ratio of 2:5:8. At the end of the year, the difference between the shares of A and C is Rs 3600, the what is the total profit and what is the share of B ?
     a) Rs 9000  , Rs 3000        
     b) Rs  12000, Rs 4500    
     c) Rs 6000, Rs 2500      
     d) Rs 8000, Rs 3250
     e) None of these
   Answer : A
   Explanation :
                Ratio of Profits = 2:5:8
                A's profit = 2x    B's profit= 5x and C's profit = 8x
             
           Difference between the share of A and C = 8x-2x = 6x= Rs 3600
                                                                                       => x=Rs 600
                  So , Total Profit = 2x +5x +8x =15x= 15 X 600 = Rs 9000
                          B's share =  5x = 5 X 600 = Rs 3000.

   Aptitude Partnerships  Solved Problem 6
    Rs 10400 is to be divided among the partners A,B and C. The ratio of their investments is $\frac{1}{2} :\frac{1}{3} :\frac{1}{4}$   . What is share of B ?
    a) Rs 1800                 b) Rs 1600                 c ) Rs 3200         d) Rs 4000   e) Rs 6500
   Answer :C
   Explanation:
                   The ratio of the investments = $\frac{1}{2} :\frac{1}{3} :\frac{1}{4} $   .

                                                          =$\frac{6}{12} :\frac{4}{12} :\frac{3}{12} $  
                                                            (Here 12 is the LCM of 2,3 and 4)
                                                           = 6 : 4 : 3
                    Therefore ratio of profits = 6 : 4 : 3
                              Share of B in total profit Rs 10400 = 10400 x $ \frac{6}{13} $   = Rs 3200
   
   Aptitude Partnerships Solved Problem 7
    A and B are partners in a business. A invests Rs 20000 for 8 months and B invests Rs 30000 for 6 months. They gains 6800 . What is the share share of B ?

    a) Rs 3000                b)Rs 3600                 c)Rs 4000             d)Rs 4500   e)Rs 8000  
   Answer : B
   Explanation:
              A and B invested their capital C1 and C2  for the time periods T2 and C2, then                                               ratio of their profits = C1T1 : C2 T2
            A invests Rs 20000 for 8 months and B invests Rs 30000 for 6 months
                    The ratio of their profits = 20000 X 8 : 30000 X 6
                                                         =8 :9
                   Share of B =    $\frac{9}{17}$ X 6800 = Rs 3600

    Aptitude Partnerships Solved Problem 8 
     A , B and C enter into a partnership . A invests Rs 7200 for 4 months, B invests Rs 2400 for whole year and C invests Rs 3600 for 8 months. The share of B in the profit is Rs 2300. What is the total profit?
    a) Rs 6900         b)Rs 6400             c)Rs 4600               d)Rs 13800   e) Rs 7800  
    Answer : A
    Explanation :
      If the capital C1 invested for the time period T1 ,and the capital C2 is invested   for the time period T2 and capital C3 is invested for the time periodT3 , then 
              Ratio of the profits = C1T1 : C2 T2 : C3T3

      Therefore, the ratio of profits   A : B : C = 7200 X 4 : 2400 X 12 : 3600 X 8
                                                             = 28800  :  28800 : 28800
                                                                        = 1 : 1 : 1
                              Share of B= 1x = 2300
                               Total Profit = 1x +1x +1x =, 3x = 3 X 2300 =Rs 6900

    Aptitude Partnerships  Solved Problem 9 

    A , B and C rented a pasture. A puts in 6 oxen for 12 months , B puts in 7 oxen for 8 months and C puts in 8 oxen for 6 months. If the rent of the filed is Rs 792, What rend is paid by C ?
   a)  Rs 162                 b)Rs 324               c)Rs 216            d)Rs 252     e)Rs 220
   Answer : C
   Explanation :  
               A puts 6 oxen for 12months
               B puts 7 oxen for 8 months
               C puts 8 oxen for 6 months.
      Therefore ratio of rents =  6 X 12 :  7 X 8 : 8 X 6
                                       = 72 : 56 :48
                                       = 9 : 8 : 6

      Rent paid by C = Rs 792 X $ \frac{6}{23}$    = 216

    Aptitude Partnerships  Solved Problem 10 
     A started a business by investing Rs. 55000.After 3 months B joined him by investing  Rs. 60000. Out of an annual profit of Rs. 42000, find the share A ?
     a) Rs 15500           b)Rs 17000               c)Rs 23100            d)Rs 18900   e)Rs 20000
   Answer : C
   Explanation:
         Ratio of their capitals = 55000 x 12 : 60000 x 9 
                                        = 660000: 540000.
                                        = 11: 9

              Share of A = Rs 42000 x $\frac{11}{20}$    = Rs 23100


    Aptitude - Partnerships  Solved Problem 11 
    A , B enter into a partnership and together start a business with contributions of Rs 30000 and Rs 40000 respectively. After 4 months , C also joins them with contribution of Rs45000. After 9 months B withdraws  his contribution. At the end of the year , the profit is Rs 24000. What is the share of B in the total profit ?
     a)Rs 5000              b)Rs 6000            c)Rs 7000             d) Rs 8000        e) Rs 8500
    Answer : B
    Explanation:
   If the capital C1 invested for the time period T1 ,and the capital C2 is invested   for the time period T2 and capital C3 is invested for the time periodT3 , then 
              ratio of the profits = C1T1 : C2 T2 : C3T3
      The ratio of profits = 30000 x 12  : 40000 x 9 : 90000 : 8
                                   = 36000 : 36000 : 72000
                                   = 1 : 1 : 2
                       Share of B in the total profit = 24000 x $ \frac{1}{4}$    =Rs 6000

   Aptitude Partnerships  Solved Problem 12
    A, Band C start a business each investing Rs. 20000. After 5 months A withdrew Rs. 5000, B withdrew Rs. 4000 and C invests Rs. 6000 more. At the end of the year, a total profit of Rs. 69900 was recorded. What is the share of B in the profit ?
     a) Rs  21200         b) Rs 20500          c) Rs 18000       d) Rs 19500     e)Rs 24500
   Answer : A
   Explanation:
        Ratio of the capitals of A, B and C.
              =( 20000 x 5 + 15000 x 7) : (20000 x 5 + 16000 x 7) :(20000 x 5  + 26000 x 7)

              = 205000 : 212000 : 282000 = 205 : 212 : 282

                           B's share = Rs. 69900 x $ \frac{212}{699} $  = Rs. 21200


    Aptitude - Partnerships  Solved Problem 13 
    A started a business with Rs. 21000 and is joined afterwards by B with Rs. 36000. After how many months did B join, if the profits at the end of the year are divided equally?
     a)  3 months         b) 4 months          c) 5 months        d) 6 months        e)7 months
     Answer : C
   Explanation:    Profit is shared at the end of the year.
           So A stays in the business for 12 months
         Let B stays in the business for x months. 
         They shared the profits equally, the P1 : P2 = 1 : 1 
        If the capital C1 is invested for the time period T1 and capital C2 is invested for the time          period T, then  
                 
                                                    
                                               
                                             => 
                                                               => 21000 x 12 = 36000 X x
x                                                        = 7
B stays in the business for 7 months. Therefore B joined the business after 5 months

   Aptitude   Partnerships  Solved Problem 14 
     A starts a business with Rs Rs 4,50,000. After 4 months , B joined the business. At the end of the year,  they shared the profits in the ratio 9 : 4 . What is the capital of B? 
      a) Rs 200000            b) Rs 250000        c) Rs 300000        d) Rs 400000    e)Rs 420000
     Answer: C
     Explanation :  
        They share the profits at the end of the year .
                   A started the business and stayed in the business for 12 months.
                   B  joined the business after 4 months , means he stayed in the business for 8 months.
                    Let the capital of B be x.   
                                                                   
                                                                  
                                                                                                                
                                                 =>  x= Rs 300000
             The capital of B is Rs 300000

     Aptitude Partnerships  Solved Problem 15 
    A invested an amount of Rs 50,000 to start a business. After 6 months, B joined him with an amount of Rs 80,000 .At the end of 3 years, they got a profit of Rs 24,500. What is the share of A?
     a) Rs 10,000         b) Rs Rs 10,500      c) Rs 15,000        d) Rs 18,000   e) Rs 19,500
       Answer : B
       Explanation:
             At the of  3 years , they shared profits.
             A started the business . So he is in the business for 36 months.
              B joined the business after 6 months . So he is in the business for 30 months

          Then ratio of their capitals = 36 x 50000 : 30 x  80000
                                                 = 3 : 4
                       A's share in the profit of Rs 24,500 = Rs 24,500 x$ \frac{3}{7}$ = Rs 10,500

    Aptitude Partnerships  Solved Problem 16 
    A , B, C and D started a partnership business. A invests 1/3 of the capital, B puts 1/4 of capital ,C invests 1/5 of the capital and D invests the remaining capital. Find the share of D out of a profit of Rs  18000 ?
     a) Rs 4000           b)Rs 5000               c) Rs 6000          d) Rs 3900    e)Rs 4200
    Answer: D
    Explanation:
      Total capital invested by A + B + C =  $\frac{1}{3} + \frac{1}{4} +\frac{1}{5} $ = $\frac{47}{60}$
                              D's capital = 1 - $\frac{47}{60}$ = $\frac{13}{60}$
                   The ratio of capitals of A,B,C and D = $\frac{1}{3} : \frac{1}{4} :\frac{1}{5} : \frac{13}{60} $
                                                                            = 20 : 15 : 12 : 13
                                    Therefore share of D = Rs 18000 X  13 /60
                                                                       =  Rs 3900
    Aptitude Partnerships  Solved Problem 17 
   A ,B and C started a partnership business by investing RS 24000 , Rs 30000 and Rs 36000 respectively. A is working partner and B and C are sleeping partners. .A gets 15% of the annual profit for his work. If B and C got Rs 17000 and Rs 20400 respectively from the annual profit as their shares, what amount did A get from the annual profit ?
     a) Rs 21000        b) Rs 23000            c) Rs 22.600       d) Rs 28000   e)Rs 27,500
     Answer : C
     Explanation:
     The ratio of capitals of A,B and C = Rs 24000 : Rs 30000 : Rs 36000
                                                                                 = 4 : 5 : 6
                          Here A is working partner and B and C are sleeping partner.
     So B and C get only profits as their shares and A gets profit and remuneration of 15% profit for his work
                              Profit ratio of B and C = Rs 17000 : Rs 20400 = 5 :6
                                                A's share of profit = $\frac{4}{15}$ < x 17000 = Rs 13600
                        85% of profit ( Because A takes 15% of profit as his share)
                                 = 17000+ 20400+13600
                                 =  Rs 41,000
                A's remuneration = 15% of total profit = $\frac{15}{85}$  x 51000  = Rs 9000
                Total amount A gets = Remuneration + profit
                                              = Rs 9000 + Rs  13600 
                                              = Rs 22,600
 For better understanding of the solved problems on Partnerships , visit Concept of Partnerships - Important Formulae
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