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Anil started a manufacturing unit with a certain amount of money. After a few months, Dheeraj became his partner, contributing three times of what Anil had contributed. At the end of the year, each was entitled to half the total profit. If Anil started the unit in January, then when did Dheeraj join as a partner?
- a)August
- b)September
- c)July
- d)October
Correct answer is option 'B'. Can you explain this answer?
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Anil started a manufacturing unit with a certain amount of money. Afte...
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Anil started a manufacturing unit with a certain amount of money. Afte...
Given information:
- Anil started a manufacturing unit with a certain amount of money.
- Dheeraj became his partner after a few months, contributing three times of what Anil had contributed.
- At the end of the year, each partner was entitled to half the total profit.
- Anil started the unit in January.
To find:
- When did Dheeraj join as a partner?
Solution:
Let's assume that Anil started the business with x amount of money.
So, Dheeraj contributed 3x amount of money.
Total amount invested in the business = x + 3x = 4x
Let's assume that the total profit earned by the business in a year = y
As per the given information, each partner was entitled to half the total profit. So, each partner got y/2 profit.
Profit received by Anil = y/2
Profit received by Dheeraj = y/2
Now, let's calculate the profit received by each partner based on their investment.
Profit received by Anil per unit of his investment = (y/2) / x
Profit received by Dheeraj per unit of his investment = (y/2) / 3x
Profit received by Anil per unit of his investment = Profit received by Dheeraj per unit of his investment
(y/2) / x = (y/2) / 3x
3 = 1/x
x = 1/3
This means that Anil invested 1/3rd of the total amount and Dheeraj invested the remaining 2/3rd of the total amount.
Now, let's find out the month in which Dheeraj joined as a partner.
Let's assume that Dheeraj joined after n months.
So, the time period for which Anil invested = 12 - n months
The time period for which Dheeraj invested = n months
Profit received by Anil = (y/2) * ((12 - n)/12)
Profit received by Dheeraj = (y/2) * (n/12)
As per the given information, both partners received equal profits.
(y/2) * ((12 - n)/12) = (y/2) * (n/12)
Solving the above equation, we get n = 9
Therefore, Dheeraj joined as a partner in the month of September.
Answer: Option (B) September.
- Anil started a manufacturing unit with a certain amount of money.
- Dheeraj became his partner after a few months, contributing three times of what Anil had contributed.
- At the end of the year, each partner was entitled to half the total profit.
- Anil started the unit in January.
To find:
- When did Dheeraj join as a partner?
Solution:
Let's assume that Anil started the business with x amount of money.
So, Dheeraj contributed 3x amount of money.
Total amount invested in the business = x + 3x = 4x
Let's assume that the total profit earned by the business in a year = y
As per the given information, each partner was entitled to half the total profit. So, each partner got y/2 profit.
Profit received by Anil = y/2
Profit received by Dheeraj = y/2
Now, let's calculate the profit received by each partner based on their investment.
Profit received by Anil per unit of his investment = (y/2) / x
Profit received by Dheeraj per unit of his investment = (y/2) / 3x
Profit received by Anil per unit of his investment = Profit received by Dheeraj per unit of his investment
(y/2) / x = (y/2) / 3x
3 = 1/x
x = 1/3
This means that Anil invested 1/3rd of the total amount and Dheeraj invested the remaining 2/3rd of the total amount.
Now, let's find out the month in which Dheeraj joined as a partner.
Let's assume that Dheeraj joined after n months.
So, the time period for which Anil invested = 12 - n months
The time period for which Dheeraj invested = n months
Profit received by Anil = (y/2) * ((12 - n)/12)
Profit received by Dheeraj = (y/2) * (n/12)
As per the given information, both partners received equal profits.
(y/2) * ((12 - n)/12) = (y/2) * (n/12)
Solving the above equation, we get n = 9
Therefore, Dheeraj joined as a partner in the month of September.
Answer: Option (B) September.
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Anil started a manufacturing unit with a certain amount of money. After a few months, Dheeraj became his partner, contributing three times of what Anil had contributed. At the end of the year, each was entitled to half the total profit. If Anil started the unit in January, then when did Dheeraj join as a partner?a)Augustb)Septemberc)Julyd)OctoberCorrect answer is option 'B'. Can you explain this answer?
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