1.

A,B invested Rs.20,000/- and Rs.25,000/- respectively in a business. The 20% of profits goes to charities. The rest being divided in proportion to their capitals out of a total profit of Rs.9000/-. The A’s share is:

**Answer: Option 'C'**

**A = Rs.20,000/- & B = Rs.25,000/-
==> A : B = 20 : 25
==> 4 : 5
Total profit = Rs.9000/-
20 % of prifit goes to charities ===> Rs.9000/- - Rs.1800/- = Rs.7200/-
remaining amount = Rs.7200/-
Total parts = 9
9 parts -----> Rs.7200/-
1 part ------> Rs.800/-
A's share ===> Rs.800/- × 4 parts = Rs.3200/-**

2.

X, Y and Z divide an amount of Rs. 11000 among themselves such that Z get half as much as Y and Y gets thrice as much as X. Find the total share of X and Y.

**Answer: Option 'D'**

**According to question
y = 3x, z = y/2 = 3x/2
x + y + z = 11000
x + 3x + 3x/2 = 11000
11x/2 = 11000
x = Rs.2000
y = Rs. 6000
x + y = 8000**

3.

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:

**Answer: Option 'D'**

**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.**

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4.

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?

**Answer: Option 'C'**

**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

5.

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

**Answer: Option 'B'**

**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**

6.

A certain amount of profit is divids between Avinash, Bhanu & Charan in the ratio of 2 : 4 : 5 respectively. If Charan got 36,000/ more than Avinash then what is Bhanu's share?

**Answer: Option 'C'**

**2 : 4 : 5
5 - 2 = 3
3 Share's ------> 36,000/-
4 Share's ------> ?
(4/3) × 36,000 = 48,000/-**

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?

**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**

8.

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?

**Answer: Option 'C'**

**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/-**

9.

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?

**Answer: Option 'D'**

**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/- **

10.

In a business A invested 3 times that of B and the period of investment of A is 2 times that of B. Then their profit ratio is:

**Answer: Option 'A'**

**share's ratio = A : B = 3 : 1
=Time ratio == A : B = 2 : 1
=profit ratio = A : B = 6 : 1 **

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11.

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:

**Answer: Option 'C'**

**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/-**

12.

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?

**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/-**

13.

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?

**Answer: Option 'C'**

**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/-**

14.

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

**Answer: Option 'B'**

**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**

15.

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.

**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**

16.

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?

**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**

17.

A and B started a partnership business investing Rs. 20,000 and Rs. 15,000 respectively. C joined them with Rs. 20,000 After six months. Calculate B's share in total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?

**Answer: Option 'B'**

**A : B : C = 20000 × 24 : 15000 × 24 : 20000 × 18 = 20 × 4 : 15 × 4 : 20 × 3
= 4 × 4 : 3 × 4 : 4 × 3
= 4:3:3
B's Share = 25000 × 3/10 = 7500/-
**

18.

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?

**Answer: Option 'C'**

**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/- **

19.

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.

**Answer: Option 'C'**

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

20.

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?

**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/- **

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