1.
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
2.
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
3.
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?
Answer: Option 'B'
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
4.
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/-
5.
In a business A invested 1/3rd of total investment in 1/3rd of period of invested, B invested 1/4th of total investment in 1/4th of period of investment and remaining was invested by C in remaining period. Then the ratio’s between their shares is:
Answer: Option 'C'
share's ratio = A : B : C = 4 : 3 : 5
=Time ratio == A : B : C = 4 : 3 : 5
=profit ratio = A : B : C = 16 : 9 : 25
6.
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
7.
A starts a business with a capital of Rs. 85,000. B joins in the business with Rs.42500 after some time. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?
Answer: Option 'B'
Let B joins for x months. Then
A:B = 85000 × 12 : x × 42500 = 3 : 1
=> 850 × 12 : 425x= 3 : 1
=> 850 × 12/ 425x = 3/1 = 3
=> 850 × 4 /425x = 1
=> 2 × 4/x = 1
=> x = 8
8.
Kamal started a business with Rs.25000 and after 4 months, Kiran joined him with Rs.60000. Kamal received Rs.58000 including 10% of profit as commission for managing the business. What amount did Kiran receive?
Answer: Option 'C'
Ratio of the profits = 25000 × 12 : 60000 × 8
= 25 × 12 : 60 × 8 = 5 × 3 : 12:2 = 5 : 4 × 2
= 5:8
Let the total profit = x.
Then Kamal received 10x/100 = x/10 as commission for managing the business
Remaining profit = x- x/10 = 9x/10 which is shared in the ration 5:8
Kamal's share = x/10 + (9x/10) × (5/13) = 58000
=> x + 9x(5/13) = 580000
=> x(1 + 45/13) = 580000
=> x ( 58/13) = 580000
=> x ( 1/13) = 10000
=> x = 130000
Kiran's share = 130000 - 58000 = 72000
9.
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/-
10.
A, B and C rent a pasture. A grazed his 35 cows for 20days, B grazed his 20 cows for 30 days and C grazed his 30 cows for 15 days. If A paid Rs. 1050 as rent , find the rent paid by them.
Answer: Option 'B'
Let the rent per cow per day be Rs.x
A's rent = 34 × 20x
700x = 1050
x = 1.5
Total rent = 1050 + 600x + 450x = 1050 + 900 + 675 = Rs. 2625/-
11.
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
12.
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/-
13.
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/-
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, 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
16.
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
17.
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.
18.
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/-
19.
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/-
20.
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?
Answer: Option 'D'
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/-
21.
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/-
22.
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
23.
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
24.
X and Y invest Rs.21000 and Rs.17500 respectively in a business. At the end of the year, they make a profit of Rs.26400. What is the share of X in the profit?
Answer: Option 'D'
Ratio of the investment = 21000 : 17500 = 210 : 175 = 42 : 35 = 6 : 5
Share of X in the profit = 26400 × (6/11) = 2400 × 6 = 14400
25.
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