## RRB NTPC - Partnership : Aptitude Test

• 1. A and B started a business by investing Rs.4000/- and Rs.5000/- respectively. Find the A’s share out of a total profit of Rs.1800:
A.) Rs.1000/-
B.) Rs.1800/-
C.) Rs.800/-
D.) Rs.400/-

A = Rs.4000/-
B = Rs.5000/-
A share 4 parts & B share 5 parts
Total 9 parts -----> Rs.1800/-
----> 1 part -------> Rs.200/-
A share = 4 parts -----> Rs.800/-

• 2. A, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, A receives:
A.) Rs. 8400
B.) Rs.11500/-
C.) Rs.11000/-
D.) Rs. 14,700

Let C = x.
Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.
So, x + x + 5000 + x + 9000 = 50000
3x = 36000
x = 12000
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.
A's share = Rs. (35000 x 21/50) = Rs. 14,700.

• 3. A,B and C started a business by investing Rs.2000/- , Rs.3000/- and Rs.4000/- respectively. Total profit is Rs.4500/-. Find the A’s share?
A.) Rs.2000/-
B.) Rs.1500/-
C.) Rs.1000/-
D.) Rs.4500/-

A = Rs.2000/- , that is 2 parts
B = Rs.3000/- , that is 3 parts
C = Rs.4000/- , that is 4 parts
Total 9 parts -------> profit (4500/-)
----->1 part -------->Rs.500/-
then A's share 2 parts ----- > Rs.1000/-

• 4. A,B and C started a business by investing Rs.1400/- , Rs.4200/- and Rs.7000/- respectively. Total profit is Rs.8100/-. Find the C's share?
A.) Rs.900/-
B.) Rs.1800/-
C.) Rs.2700/-
D.) Rs.4500/-

A = Rs.1400/- , that is 1 parts
B = Rs.4200/- , that is 3 parts
C = Rs.7000/- , that is 5 parts
Total 9 parts -------> profit (8100/-)
1 part --------> Rs.900/-
then C's share
5 parts -----> Rs.4500/-,

• 5. 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/-

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/-

• 6. A,B and C started a business in which A invested Rs.10000/- for 1year, B invested Rs.20000/- for 2 years, C invested Rs.30000/- for 3 years. At the end of the profit received by them is Rs.5600/-. What is C’s share?
A.) Rs.1600/-
B.) Rs.400/-
C.) Rs.3600/-
D.) Rs.2000/-

A = Rs.10000/- per 1 year
B = Rs.20000/- per 2 years
C = Rs.30000/- per 3 years
= 10000 × 1 : 20000 × 2 : 30000 × 3
= 1 : 4 : 9
Total = 14 parts -----> Rs.5600/- (profit)
= 1 part ------> Rs.400/-
Then, C's share is
= 9 part = Rs.400/- × 9 parts = Rs.3600/-

• 7. 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

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

• 8. If 4 (P's Capital ) = 6 ( Q's Capital ) = 10 ( R's Capital ) , then out of the total profit of Rs 4650 , R will receive
A.) 700
B.) 900
C.) 600
D.) 750

Let P's capital = p, Q's capital = q and R's capital = r
Then
4p = 6q = 10r
=> 2p = 3q = 5r
=>q = 2p/3
r = 2p/5
P : Q : R = p : 2p/3 : 2p/5
= 15 : 10 : 6
R's share = 4650 × (6/31) = 150 × 6 = 900

• 9. In a business, A and C invested amounts in the ratio 2 : 1 , whereas the ratio between amounts invested by A and B was 3 : 2 . If Rs 157300 was their profit, how much amount did B receive?
A.) 48600
B.) 48400
C.) 48500
D.) 44800

Assume that investment of C = x
Then, investment of A = 2x
Investment of B = 4x/3
A:B:C = 2x : 4x/3 : x = 2 : 4/3 : 1 =6 : 4 : 3
B's share = 157300 × 4/(6+4+3) = 157300 × 4/13
= 12100 × 4 = 48400

• 10. 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

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

• 11. A,B and C started a business in which A invested Rs.20000/- for 2year, B invested Rs.30000/- for 3 years, C invested Rs.40000/- for 4 years. At the end of the profit received by them is Rs.11,600/-. What is B’s share?
A.) Rs.3600/-
B.) Rs.6400/-
C.) Rs.3200/-
D.) Rs.3200/-

A = Rs.20000/- per 2 year
B = Rs.30000/- per 3 years
C = Rs.40000/- per 4 years
= 20000 × 2 : 30000 × 3 : 40000 × 4
= 4 : 9 : 16
Total = 29 parts -----> Rs.11600/- (profit)
= 1 part ------> Rs.400/-
Then, B's share is
= 9 part = Rs.400/- × 9 parts = Rs.3600/-

• 12. A,B and C started a business in which A invested Rs.2000/- for 1year, B invested Rs.3000/- for 1 1/2 years, C invested Rs.4000/- for 2 years. At the end of the profit received by them is Rs.14500/-. What is C’s share?
A.) Rs.2000/-
B.) Rs.4500/-
C.) Rs.8000/-
D.) Rs.1600/-

A = Rs.20000/- per 12 months
B = Rs.30000/- per 18 months
C = Rs.40000/- per 24 months
= 20000 × 12 : 30000 × 18 : 40000 * 24
= 4 : 9 : 16
Total = 29 parts -----> Rs.14500/- (profit)
= 1 part ------> Rs.500/-
Then, C's share is
= 16 part = Rs.500/- × 16 parts = Rs.8000/-

• 13. A started a business by investing Rs.4000/-. After 4 months B joined by investing Rs.5000/- At the end of the year, there was a profit of Rs.8800/-. What is A’s share?
A.) Rs.4000/-
B.) Rs.4500/-
C.) Rs.4800/-
D.) Rs.5600/-

A = Rs.4000/- per 12 months
B = Rs.5000/- per 8 months
= 4000 × 12 : 5000 × 8
= 6 : 5
Total = 11 parts -----> Rs.8800/- (profit)
= 1 part ------> Rs.500/-
Then, A's share is
= 6 part = Rs.800/- × 6 parts = Rs.4800/-

• 14. A started a business by investing Rs.5000/-. After 4 months B joined by investing Rs.4000/- After 2 months C joined by investing Rs.3000/-. At the end of the year, they got a profit of Rs.5500/-. What is A’s share?
A.) Rs.900/-
B.) Rs.1600/-
C.) Rs.3600/-
D.) Rs.3000/-

A = Rs.5000/- per 12 months
B = Rs.4000/- per 8 months
C = Rs.3000/- per 6 months
= 5000 × 12 : Rs.4000 × 8 : Rs.3000 × 6
= 30 : 16 : 9
Total = 55 parts -----> Rs.5500/- (profit)
= 1 part ------> Rs.100/-
Then, A's share is
= 30 part = Rs.100/- × 30 parts = Rs.3000/-

• 15. 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/-

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/-

• 16. A and B starts a business investing Rs.85000 and Rs.15000 respectively. Find out the ratio in which the profit s should be shared.
A.) 17:4
B.) 16:3
C.) 17:3
D.) 3:11

Here A's and B's capitals are there for equal time. Hence
A : B = 85000 : 15000
= 85 : 15
= 17 : 3

• 17. 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

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

• 18. A , B , C started a partnership business by investing Rs 27000 , 72000 , 81000 respectively. At the end of the year , the profit were distributed among them. If C's share of profit is 36000, What is the total profit?
A.) 80000
B.) 90000
C.) 70000
D.) 110000

A:B:C = 27000:72000:81000
= 3:8:9
Let the total profit= p
Then p × 9/20 = 36000
=> p = 36000 × 20/9 = 80000

• 19. 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

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

• 20. A starts a business with Rs. 3500. After 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. B's contribution in the capital is
A.) 7000
B.) 9000
C.) 10000
D.) 6000

Ratio in which profit is divided = 2:3
Assume that B's contribution to the capital = b
=> 3500 × 12 : b × 7 = 2:3
=> 3500 × 12/7b = 2/3
=> b = (3500 × 12 × 3)/(2 × 7) = 500 × 6 × 3 = 9000

• 21. 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, How many months B was in the business?
A.) 4 Months
B.) 7 Months
C.) 5 Months
D.) 6 Months

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 = Rs.5000/- per 12 Months
B = Rs.4000/- per x Months
4000 × 12 : 5000 × 8 = 3 : 1
=> 6 : 5 = 3 : 1
=> 3x = 15
=> x = 5 Months

• 22. 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

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

• 23. A,B started a business by investing Rs.10000/- and Rs.20000/- respectively. After 1year B withdrew Rs.5000/- and A invested Rs.5000/- more. At the end of 2 years they got total Profit Rs.6000/-. What is A’s share?
A.) Rs.3500/-
B.) Rs.2800/-
C.) Rs.2000/-
D.) Rs.2500/-

A's Share = Rs.10000/- per first 1 year, Next year Rs.5000/- added
= Rs.10000/- × 1 + Rs.15000 × 1 = 25000
B's Share = Rs.20000/- per first 1 year, Next year Rs.5000/- reduced
= Rs.20000/- × 1 + Rs.15000/- × 1 = Rs.35000/-
Then,A's part= 25 : B's part= 35
Total 60 parts -----> Rs.6000/-
1 part ------> Rs.100/-
Then, A's share is
25parts = Rs.100/- × 25 parts = Rs.2500/-

• 24. In a business, A,B and C inversed Rs.10,000/-,Rs.20,000/- and Rs.30,000/- respectively. After 1 year A adds Rs.5000/- to the initial investment. B and C withdrew Rs.5000/- and Rs.10,000/- respectively. After 2 years the total profit is Rs.7700/-. What is A’s share?
A.) Rs.350/-
B.) Rs.3500/-
C.) Rs.1750/-
D.) Rs.700/-

A's Share = Rs.10000/- per first 1 year, Next year 5000/- added
= Rs.10000/- × 1 + Rs.15000/- × 1 = Rs.25000/-
B's Share = Rs.20000/- per first 1 year, Next year 5000/- reduced
= Rs.20000/- × 1 + Rs.15000/- × 1 = Rs.35000/-
C's Share = Rs.30000/- per first 1 year, Next year 10000/- reduced
= Rs.30000/- × 1 + Rs.20000/- × 1 = Rs.50000
Then,A's part = 25 : B's part = 35 : C's part = 50
===> 5 : 7 : 10
Total 22 parts -----> Rs.7700/-
2 parts ------> Rs.700/-
Then, A's share is
5 parts = Rs.350/- × 5 parts = Rs.1750/-

• 25. 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/-

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/-