aptitude : : partnership
 
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   Exercise 2
   Exercise 3
   Exercise 1
1.
Three laborers work for 5 hours, 6 hours and 7 hours respectively in a field and get wages in the proportion of time of working in the field. Three days after they increase their working hours by 1 hour. 4 days after they increase their working hours ,work in the field gets finished. If their total wages is Rs. 276, find the share of wages earned by each of them.
 
A.
Rs. 78, Rs, 92, Rs. 106

B.

Rs.88, Rs. 87, Rs. 101
C.
Rs. 80, Rs . 90, Rs. 106
D.
Rs.81, Rs. 95, Rs. 100
   
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Answer: A
Explanation :
Total  working  hours  of  1st labourer  = 5 hours  for 3 days + 6 hours  or 4 days
                                                                     = 5 X  3 + 6 X 4 = 15 + 24
                                                                     = 39 hours
Total  working  hours  of  2nd labourer = 6 hours  for 3 days + 7 hours  for 4 days
                                                                     =6x3+7x4
                                                                     =  18 + 28 = 46 hours
Total working hours of the third labourer = 7 hours for 3 days + 8 hours for 4 days
                                                                         =7x3+8x4
                                                                         = 21 + 32 = 53 hours
Wages will be divided among them in the ratio of their working  hours
Ratio of  their  working  hours
                                                       = 39  : 46  : 53
Sum  of  proportionals               = 39 + 46 + 53 =  138
Total  wages                                = Rs. 276
Therefore, Wages for the 1st labourer
                                                       = 39/138 X 276 = Rs. 78 
Wages for the  2nd labourer     = 46/138 X 276 = Rs. 92
Wages for the  3rd labourer      = 53/138 X 276 = Rs. 106
 
Therefore they will get wages of Rs. 78, Rs. 92 and Rs. 106 respectively.
 
 






 
2.
A, B and C started a business in partnership with respective investment of Rs. 20000, Rs. 18000 and Rs. 12000. A and B are active partners and therefore they get an additional profit of 12% and 8% respectively for supervision and other related work they do for improvement of the trade. Rest of the profit is divided among them in the proportion of their capitals. If profit made by A is Rs. 648 more than B, find the profit earned by each of them.
 
A.
Rs. 3960, Rs. 3312, Rs. 1728

B.

Rs. 4960, Rs.3312, Rs. 1728
C.
Rs. 3690, Rs. 3132, Rs. 1820
D.
Rs. 5960, Rs. 3600, Rs. 1750
   
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Answer: A
Explanation :
Suppose total profit in the business = Rs. x
 
              Additional profit of A = 12% of x = 12/100 X x
                                                                       =  3x/25
              Additional profit of B  = 8% of x = 8/100 X x
                                                    = Rs. 2x/25
Remaining profit  = x-(3x/25 + 2x/25) = x- 5x/25
                                =  Rs. 4x/5
 
Remaining profit will be divided in the proportion of their capitals
 
Therefore, Ratio of their capitals = 2000 : 18000 : 12000
                                                           = 10 : 9 : 6
Sum of proportionals  = 10 + 9  + 6 = 25
Therefore,   A's profit  = 10/25 X 4x/5 = Rs. 40x/125  
                      B's profit  =  9/25  X 4x/5 = Rs. 36x/125        
                      C's profit  =  6/25  X 4x/5 = Rs. 24x/125
Therefore,   A's total profit = 40x/125 + 3x/25 = Rs. 55x/125
                      B's total profit = 36x/125 + 2x/25 = Rs. 46x/125
 
According to question : 
 
A's profit is Rs. 648 more than B's profit 
 
Therefore,                    55x/125 = 46x/125 + 648
 
or,                                  9x/125   = 648 or x = 648X125/9
                                                      = Rs. 9000
Therefore,                    A's profit = 55/125 X 9000 = Rs. 3960
                                       B's profit = 46/125 X 9000 = Rs. 3312
                                       C's profit = 24/125 X 9000 = Rs. 1728
 
Therefore, They will get Rs. 3960, Rs. 3312 and Rs. 1728 respectively as profit.  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 






 
3.
A, B and C started a business in partnership. A invested Rs. 4000 for 8 months and Rs. 6000 for 4 months. B invested  Rs. 3000 for 6 months and Rs. 5000 for next 6 months of the year while C invested Rs. 3000 for whole of the year. If at the end of year, total profit is Rs. 7000, what will be the shares of A, B and C in the profit?
 
A.
Rs. 2800, Rs.2400, Rs.1800

B.

Rs. 2500,Rs.2600,Rs.1900
C.
Rs. 2600 , Rs. 2500, Rs. 1900
D.
Rs.2000,Rs. 2700, Rs. 2300
   
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Answer: A
Explanation :
Capital  of A in the business  = Rs. 4000 for 8 months + Rs. 6000 for 4 months
                                                     =4000x8+6000x4
                                                     = 32000 + 24000
                                                     = Rs. 56000 for 1 month
Capital of B in the business= Rs. 3000 for 6 months + Rs. 5000 for 6 months
                                                      = 3000 X 6 + 5000 X 6
                                                      = 18000 + 30000
                                                      = Rs. 48000 for 1 month
Capital of C in the business    = Rs. 3000 x 12
                                                      = Rs. 36000 for 1 month
Therefore, Ratio  of  their  capitals  = 56000  : 48000  : 36000
                                                               = 14 : 12 : 9
Therefore, Ratio  of  their  profits     =  14 :  12 : 9
Sum of  proportionals                        =  14 +  12 + 9 = 35
Total  profit                                           = Rs.  7000
 
Therefore, Share of A in the profit = 14/35 X 7000 = Rs 2800
                    Share of B in the profit = 12/35 X 7000 = Rs 2400
                    Share of C in the profit = 9/35   X 7000 = Rs 1800
 
Therefore their profits will be Rs. 2800, Rs. 2400 and Rs. 1800 respectively. 
 
 
 






 
4.
Amit, Sumeet and Suresh started a business with capitals in the ratio of 2 : 3 : 4. Amit took back half of his investment after 3 months and Sumeet took back one-­third portion of his investment after 4 months. If at the end of year, Suresh gets a profit of Rs. 3200, what is the total profit in the business?
 
A.
Rs. 6076 (2/3)

B.

Rs. 6066 (2/3)
C.
Rs. 8000
D.
Rs. 8333 (1/3)
   
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Answer: B
Explanation :
Suppose Amit, Sumeet and Suresh invested Rs. 2x, Rs.3x,
and Rs. 4x respectively.
 
Therefore, Half of the capital of Amit = 2x/2 = Rs. x
One-third portion of capital of sumeet = 3x/3 = Rs. x
 
Therefore, Investement by Amit = Rs. 2x for 3 months and Rs. x for 9 months
Therefore, Capital of Amit = 2x X 3 +x X 9 = 6x + 9x = 15x for 1 month 
 
Investment  by sumeet = Rs. 3x for 4 months and Rs. x for 8 months  
Therefore, Capital of Sumeet = 3x X 4 + 2x X 8
                                                     =  12x +  16x
                                                     = Rs. 28x for  1 month
Investment  by  Suresh  = Rs. 4x for  12 months
        Capital  of  Suresh  = Rs. 4x X 12
                                            = Rs. 48x for  1 month
Therefore, Total  investment  in  the  business
                                            = 15x + 28x + 48x = 91x
Therefore, Profit of Suresh = Rs.  3200
 
Therefore,           48x = 3200 or x = 3200/48
Therefore, Total profit in the business  = 91X 3200/48 = Rs. 6066 (2/3)






 
5.
A started a business with an investment of Rs. 4000. B joined him after 4 months and C joined him after 5 months. At the end of year they get profit in the ratio of 3 : 4 : 7. Find the ratio of capitals invested in the business by B and C.
 
A.
1:2

B.

2:1
C.
3:2
D.
1:3
   
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Answer: A
Explanation :
Suppose  B  and  C invest  Rs. x  and Rs. y  respectively
 
Therefore,  Capital  of  A =  Rs. 4000 x  12
                                             = Rs. 48000 for 1 month
                     Capital  of  B = Rs. x X 8
                                             =  Rs.  8x for  1 month
                     Capital  of  C = Rs. y  x 7
                                             = Rs. 7y for 1 month
Therefore, Ratio of their profits = 48000  : 8x : 7y
 But given ratio of the profits = 3 : 4 : 7
                                      8x : 7y = 4 : 7
or,                                     8x/7y = 4/7 or x/y = 4/7 X7/8 = 4/8 = 1/2 
or,                                  x :y = 1:2
 
Therefore, Ratio of capitals invested by B and C is 1:2.
 
 
 
 






 
6.
Premchand, Nanak and Prabhat together rented a house for 2 years and settled to pay Rs. 1368 as rent. They lived together in this house for 5 months. Then Prabhat left the house and went away . 8 months after Nanak also went  away  and  left the  house for Premchand  to live alone. How  much  did Premchand  pay  as rent of this  house?
 
A.
Rs. 1025

B.

Rs. 950
C.
Rs. 880
D.
Rs. 780
   
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Answer: B
Explanation :
While the three persons live together, their 1 month's rent
 
       = 1368/24 = Rs. 57
 
Therefore, 1 month's rent to be paid by each of them
        
        = Rs. 57/3 = Rs. 19
 
In the second case :Premchand and Nanak live together
Therefore, Rent per month  paid  by  each  of  them
 
   
         = Rs. 57/2 = Rs. 28.50
 
 
In the third case : Premchand lives alone
Therefore, Rent per  month  paid by  him = Rs. 57
Therefore, Total  rent paid  by  Premchand
                                 = 19 X  5 + 28.50 X  8 + 57 X  11
                                 = 95 + 228.00 + 627 = Rs. 950
 






 
7.
A, B and C started a business with the investment of Rs. 5000, Rs, 6000 and Rs. 4000 respectively. A is an active partner and therefore he gets 30% of the profit separately. Rest of the profit in divided in the ratio of their capitals. If at the end of year, A's profit is Rs. 200 more than the sum of the profits made by B and C, find the profit made by each of them.
 
A.
Rs. 1620; Rs. 1242, Rs. 1178

B.

Rs.1720, Rs .1252, Rs.1228
C.
Rs.1510, Rs.1187, Rs.1133
D.
Rs. 1600, Rs. 840, Rs. 560
   
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Answer: D
Explanation :
Suppose total profit in the business = Rs. x
      Separate profit  for A = 30%  of  total  profit
                                            = 30X x/100 = Rs. 3x/100
 Remaining profit             = x - (3x/10) = Rs. 7x/10  
Ratio of their capitals      = 5000:6000:4000
                                            = 5: 6 : 4
Sum of proportionals      = 5+6+4 = 15
 Therefore,      Profit of A = 5/15X7x/10 = Rs.7x/30
                          Profit of B = 6/15X7x/10 = Rs.7x/25
                          Profit of C = 4/15X7x/10 = Rs.14x/75
Therefore, Total profit of A = 3x/10 + 7x/30 = 9x + 7x/ 30
                                                = 16x/30 = Rs. 8x/15 
 
According to question:
                                          8x/15 = 7x/25 + 14x/75 + 200
or,                                      8x/15 = 21x+14x/75 + 200
or,                                      8x/15 = 35x/75 + 200
or,                                     (8x/15)-(35x/75) = 200
or,                                      40x-35x/75 = 200
or,                     5x/75 = 200
or,                     x = 200X75/5 = 3000
 
Therefore, Total profit in the business = Rs. 3000
Therefore,                    A's profit = 8x3000/15 = Rs. 1600
                                       B's profit = 7X3000/25 = Rs. 840
                                       C's profit = 14X3000/75 = Rs. 560 
Therefore, A,B and C made profits of Rs. 1600, Rs. 840 and Rs. 560 respectively.
 
 
 






 
8.
A, B and C together took under lease a pasture ground for Rs. 888. If in this pasture ground A put his 20 sheeps out to graze for 2V2 months, B put his 30 sheeps out to graze for 4 months and C put his 36 sheeps out to graze for 31/2 months, find the lease amount paid by each of them.
 
A.
Rs. 205, Rs. 315, Rs. 378

B.

Rs.150, Rs. 360, Rs . 378
C.
Rs.170, Rs. 360, Rs . 358
D.
Rs. 228, Rs. 360, Rs. 300
   
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Answer: B
Explanation :
A, B and C put their sheeps out to graze for different periods
Therefore, Number of sheeps put out to graze by A for 1 month                  
                                   = 20X 21/2 = 20X5/2 = 50
 
Number  of  sheeps put  out to graze by  B for  1 month
                                    = 30 X  4 =  120
Number  of  sheeps put  out to graze by  C for  1 month
                                    = 36 x 31/2 = 126
Therefore, Ratio of  sheeps put  out to graze by  A, B and C
                                    = 50 : 120 : 126
                                    = 25  : 60 : 63
Sum  of  proportionals  = 25 + 60 + 63 =  148
   Total  lease  amount  = Rs.  888
Therefore, Amount paid by A = 25/148X 888 = Rs. 150
Amount paid by                     B = 60/148X 888 = Rs. 360
Amount paid by                     C = 63/148X 888 = Rs. 378
Therefore, They paid Rs. 150, Rs. 360 and Rs. 378 respectively
 






 
9.
Neeraj and Birju are partners in a business. They divide between  them  the  profit incurred  in  the  business  in the business in such a proportion that 2/5 portion of the profit gained by Neeraj is equal to 1/3 portion of the profit gained by Birju. If total profit in the business is Rs. 1210, find the profit earned by  Birju.
 
A.
Rs. 780

B.

Rs. 550
C.
Rs. 680
D.
Rs. 590
   
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Answer: B
Explanation :
According to question :
2/5 portion of profit made by Neeraj = 1/3rd portion of profit  made by Birju
Therefore, Ratio between  profits  of Neeraj  and Birju
                             = 2/5:1/3 = 6:5
 
Where  total  profit  = Rs.  1210
In  the  above  proportion,  sum  of  proportionals
                                  =6+5=11
Therefore, Share of Birju in the profit = 55/11X 1210 = Rs. 550
 






 
10.
Two partners invested Rs. 12500 and Rs. 8500 respectively in a business and decided that 60% of the profit incurred from the business will be equally divided between them while remaining profit will be assumed as interest on their capitals . If one of the partners gets Rs. 300 more profit than the other, what is the total profit int he business?
 
A.
Rs. 3937.50

B.

Rs. 4940.50
C.
Rs. 3936.50
D.
Rs. 4156
   
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Answer: A
Explanation :
Suppose total  profit  in  the business  = Rs. x
Therefore, 60%  of  total  profit  = 60% of x =  Rs. 3x/5
 
Therefore, The two partners will get profit of Rs. 3x/10 and Rs. 3x/10 respectively.
Therefore, Remaining  profit = x- (3x/5) = Rs. 2x/5
The remaining profit assumed as interest on the capital will  be  divided  in  the  proportion  of  their  capitals Ratio between  their capitals =  12500 : 8500 = 25 : 17
          Sum  of  proportionals  = 25 +  17 = 42
Therefore, 1st partner's = 25/42 X 2x/5 = Rs. 5x/21
                    2nd partner's = 17/42 X 2x/5 = Rs. 17x/105
 
According to question:
                                          3x/10+ 5x/21 = 3x/10 + 17x/105 + 300
 
Therefore, 8x/105 = 300 OR x = 105X300/8
                                 = Rs. 3937.50
Therefore, Total profit in the business = Rs. 3937.50.  






 

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