1.

X starts a business with Rs.45000. Y joins in the business after 3 months with Rs.30000. What will be the ratio in which they should share the profit at the end of the year?

**Answer: Option 'B'**

**Ratio in which they should share the profit
= Ratio of the investments multiplied by the time period
= 45000 × 12: 30000 × 9
= 45 × 12: 30 × 9
= 3 × 12: 2 × 9
= 2:1**

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2.

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?

**Answer: Option 'A'**

**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/- **

3.

Suresh started a business with Rs.20,000. Kiran joined him after 4 months with Rs.30,000. After 2 months, Suresh withdrew Rs.5,000 of his capital and 2 more months later, Kiran brought in Rs.20,000 more. What should be the ratio in which they should share their profits at the end of the year?

**Answer: Option 'A'**

**Here capital is not the same.
Suresh invest 20000 for initial 6 months and 15000 for the next 6 months.
Hence his term of ratio
=( 20000 × 6 + 15000 × 6)
Kiran invest Rs.30000 for 4 months and Rs.50000 for next 4 months.
Hence his term of ration
= (30000 × 4 : 50000 × 4)
Suresh : Kiran = ( 20000 × 6 + 15000 × 6) : (30000 × 4 : 50000 × 4)
= (20 × 6 + 15 × 6) : (30 × 4 + 50 × 4)
= (20 × 3 + 15 × 3) : (30 × 2 : 50 × 2)
= 105:160
= 21:32**

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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.

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?

**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/-

6.

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

**Answer: Option 'B'**

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

7.

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/-**

8.

A,B started a business by investing Rs.4000/- and Rs.5000/-. A is working and B is sleeping partner. A gets 10% of profits for managing, the rest being divided in proportion to their capitals out of a total profit of Rs.9,000/-. The money received by B is:?

**Answer: Option 'D'**

**A = Rs.4000/-
B = Rs.5000/-
Then, A : B = 4 : 5
Total profit = Rs.9000/-
10 % of 9000 = Rs.900/-
A's Salary = Rs.900/-
remaining amount = 8100/-
Total parts = 9
9 parts -----> Rs.8100/-
1 part ------> Rs.900/-
B's share = 5 parts
= 5 parts -----> Rs.4500/-**

9.

A, B, C rent a pasture. If A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing and the rent of the pasture is Rs. 175, then how much amount should C pay as his share of rent?

**Answer: Option 'C'**

**A : B: C = 10 × 7 : 12 × 5 : 15 × 3 = 2 × 7 : 12 × 1 : 3 × 3 = 14 : 12 : 9
amount that C should pay = 175 × (9/35) = 5 × 9 = 45**

10.

A and B invest in a business in the ratio 3: 2. Assume that 5% of the total profit goes to charity. If A's share is Rs. 855, what is the total profit?

**Answer: Option 'C'**

**Assume that the total profit is x.
Since 5% goes for charity, 95% of x will be divided between A and B in the ratio 3: 2
=> A's profit = (95x/100) × (3/5) = 855
=> 95x/100 = 855 × 5/3 = 285 × 5 = 1425
=> x = 1425 × 100/95 = 285 × 100/19 = 1500
Hence the total profit = 1500**

11.

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?

**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/- **

12.

A, B and C start a business with their investments in the ratio 3 : 2 : 1. A leaves after 6 months and B leaves after 9 months. Find the ratio of profits at the end of a year.

**Answer: Option 'B'**

**Ratio of the profits = (3 × 6) : 2 × 9) : (1 × 12)
=> 18 : 18 : 12 = 3 : 3 : 2**

13.

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?

**Answer: Option ''**

**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/- **

14.

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/-**

15.

Ganesh starts a business investing Rs. 30000. After a year, Ramesh joins him with a capital of Rs. 40000 and Suresh joins them after another year with Rs. 50000. The profit at the end of three years is Rs. 44000. Find Ramesh's share.

**Answer: Option 'C'**

**Ratio of their investments after 3 years = (3000 × 3) : (40000 × 2) : (50000) = 9 : 8 : 5
Ramesh's share = (8/22) × 44000 = Rs. 16000**

16.

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**

17.

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?

**Answer: Option 'A'**

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

18.

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?

**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**

19.

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/- **

20.

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**

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