RRB NTPC - Partnership : Aptitude Test

41.

P , Q, R enter into a partnership & their share are in the ratio 1/2 : 1/3 : 1/4 , after two months , P withdraws half of the capitals & after 10 months , a profit of Rs 378 is divided among them . What is Q's share?

   A.) 144
   B.) 154
   C.) 164
   D.) None of these

Answer: Option 'A'

The ratio of their initial investment = 1/2 : 1/3 : 1/4
= 6 : 4: 3
Let's take the initial investment of P, Q and R as 6x, 4x and 3x respectively
A:B:C = (6x × 2 + 3x × 10) : 4x × 12 : 3x × 12 
= (12 + 30) : 4 × 12 : 3 × 12
=(4 + 10) : 4 × 4 : 12
= 14 : 16 : 12
= 7 : 8 : 6
B's share = 378 × (8/21) = 18 × 8 = 144

42.

A starts a business with Rs.40,000. After 2 months, B joined him with Rs.60,000. C joined them after some more time with Rs.1,20,000. At the end of the year, out of a total profit of Rs.3,75,000, C gets Rs.1,50,000 as his share. How many months after B joined the business, did C join?

   A.) 5 months
   B.) 4 months
   C.) 6 months
   D.) 7 months

Answer: Option 'B'

Assume that C was there in the business for x months
A:B:C = 40000 × 12 : 60000 × 10 : 120000 × x 
= 40 × 12 : 60 × 10 : 120x = 40 : 5 × 10 : 10x 
= 8 : 10 : 2x 
= 4 : 5 : x
C's share = 375000 × x/(9+x) = 150000
=> 375x/(9+x) = 150
=> 15x = 6(9+x)
=> 5x = 18 + 2x
=> 3x = 18 
=> x = 18/3 = 6
It means C was there in the business for 6 months. Given that B joined the business 
after 2 months. Hence C joined after 4 months after B joined

43.

Ravi, Naresh and Raju started a business in which Ravi invested Rs. 18,000/-, Naresh  invested Rs. 22,000/ and Raju invested Rs. 30,000/-. At the end of the year profit received by them is Rs. 14,000/-. What is the difference between the profits Ravi and Raju?

   A.) Rs. 2500/-
   B.) Rs. 2400/-
   C.) Rs. 2300/-
   D.) Rs. 2100/-

Answer: Option 'B'

18000 : 22000 : 30000
    9    :  11  :  15
The difference between Ravi and Raju  15 - 9 = 6
total 35  --------> 14000
only  6 ---------> ?
(6/35) × 14,000 = 2400/-

44.

A,B started a business in which A invested Rs.10000/- for 1year, B invested Rs.20000/- for 2 years. At the end of the profit received by them is Rs.5000/-. What is A’s share?

   A.) Rs.4000/-
   B.) Rs.3000/-
   C.) Rs.2000/-
   D.) Rs.1000/-

Answer: Option 'D'

A = Rs.10000/- per 1 year 
B = Rs.20000/- per 2 years 
= 10000 × 1 : 20000 × 2 
= 1 : 4 
Total = 5 parts -----> Rs.5000/- (profit)  
      = 1 part ------> Rs.1000/- 
Then, A's share is 
      = 1 part = Rs.1000/- 

45.

A started a business by investing Rs.10000/-.After 1 year B joined by investing Rs.15000/- After 6 months C joined by investing Rs.2400/-. At the end two year, they got a profit of Rs.47000/-. What is A’s share? 

   A.) Rs.2000/-
   B.) Rs.1500/-
   C.) Rs.20000/-
   D.) Rs.15000/-

Answer: Option 'C'

A = Rs.10000/- per 24 months
B = Rs.15000/- per 12 months 
C = Rs.24000/- per 6 months 
= 10000 × 24 : 15000 × 12 : 24000 × 6 
= 20 : 15 : 12 
Total = 47 parts -----> Rs.47000/- (profit)  
         = 1 part ------> Rs.1000/- 
Then, A's share is 
         = 20 part = Rs.1000/- × 20 parts = Rs.20000/-

46.

P and Q invested in a business. The profit earned was divided in the ratio 2 : 3. If P invested Rs 40000, the amount invested by Q is 

   A.) 40000
   B.) 60000
   C.) 50000
   D.) 70000

Answer: Option 'B'

Let the amount invested by Q = q 
40000 : q = 2 : 3 
=> 40000/q = 2/3 
=> q = 40000 × (3/2) = 60000

47.

A and B started a partnership business investing capital in the ratio of 3 : 5. C joined in the partnership after six months with an amount equal to that of B. At the end of one year, the profit should be distributed among A, B and C in --- proportion. 

   A.) 6 : 10 : 5
   B.) 10 : 5 : 4
   C.) 3 : 4: 5
   D.) 9 : 5 : 4

Answer: Option 'A'

Initial investment capital ratio of A and B = 3 : 5
Hence we can assume that initial capital of A and B are 3x and 5x respectively.
Amount that C invest after 6 months = 5x (Since it is equal to B's investment)
Ratio in which profit should be distributed after 1 year = 3x × 12 : 5x × 12 : 5x × 6
=> 3 × 12 : 5 × 12 : 5 × 6 
= 6 : 10 : 5

48.

In a business, A,B inversed Rs.10,000/-,Rs.20,000/- respectively. After 4 months A adds Rs.5000/- to his initial investment and B withdrew Rs.5000/- from his initial investment. At the end of the year total amount of profit they got is Rs.5400/-. What is A’s share?

   A.) Rs.600/-
   B.) Rs.3000/-
   C.) Rs.4500/-
   D.) Rs.2400/-

Answer: Option 'D'

A's Share = Rs.10000/- per first 4 maonth + Next 8 months Rs.5000/- added 
= 10 × 4 + 15 × 8 = 40 + 120 = 160 
B's Share = Rs.20000/- per first 4 months + Next 8 months Rs.5000/- added 
= 20 × 4 + 15 × 8 = 200   
Then,A's part= 160 : B's part= 200 
==> 4 : 5 
 Total 9 parts -----> Rs.5400/- 
           = 1 part ------> Rs.600/- 
Then, A's share is 
= 25parts = Rs.600/- × 4 parts = Rs.2400/- 

49.

A invested Rs 76000 in a business. After few months, B joined him with Rs 57000. The total profit was divided between them in the ratio 2 : 1 at the end of the year. After how many months did B join?

   A.) 3
   B.) 4
   C.) 5
   D.) 6

Answer: Option 'B'

Answer: Option 'B' 
Assume that B joins for x months . Then
A : B = 76000 × 12 : 57000 × x = 2:1
=> 76 × 12 : 57x = 2:1
=> 76 × 12/57x = 2/1 = 2
=> x = 76 × 12/57 × 2 = 76 × 4/19 × 2 = 8
Hence B was there in the business for 8 months, or joined after 12-8 = 4 months

50.

A began a business with Rs.5000/- and was joined afterwards by B with Rs.4000/-. If the profits at the end of the year were divided in the ratio 3:1, B joined the business after:?

   A.) 4 Months
   B.) 7 Months
   C.) 5 Months
   D.) 6 Months

Answer: Option 'B'

Note : 
1) Share's ratio is always equal to profit ratio
2) When two ratios are equal, then the cross products of the ratios are equal. 
That is, for the proportion, a:b = c:d , a × d = b × c 
A = 5000/- per 12 Months
B = 4000/- per × Months 
4000 * 12 : 5000 × 8 = 3 : 1 
=> 6 : 5 = 3 : 1  
=> 3x = 15 
=> x = 5 Months 
Then, B joined the business after = 12 - x ==> 12 - 5 ==> after 7 Months


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