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Akash started a business with Rs. 80,000 and after some months Rahul joined him with Rs. 75000. If the profit at the end was distributed in the ratio of 8 ∶ 5, then after how many months did Rahul join Akash? (Assume Akash has worked throughout the year).
- a)4
- b)6
- c)8
- d)2
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Akash started a business with Rs. 80,000 and after some months Rahul j...
GIVEN:
Capital of Akash = Rs. 80,000 and time = 12 months
Capital of Akash = Rs. 80,000 and time = 12 months
FORMULA USED:
Profit = Capital × time,
Profit = Capital × time,
CALCULATION:
Let the number of months that Rahul has worked be ‘x’.
Capital of Rahul = Rs. 75,000 and time = x months,
The ratio of profit of Akash and Rahul = 8 ∶ 5,
⇒ 8/5 = (80,000 × 12)/(75,000 × x)
⇒ x = (80,000 × 12 × 5)/(75,000 × 8)
⇒ x = 8 months
∴ After 4 months Rahul joined Akash.
Let the number of months that Rahul has worked be ‘x’.
Capital of Rahul = Rs. 75,000 and time = x months,
The ratio of profit of Akash and Rahul = 8 ∶ 5,
⇒ 8/5 = (80,000 × 12)/(75,000 × x)
⇒ x = (80,000 × 12 × 5)/(75,000 × 8)
⇒ x = 8 months
∴ After 4 months Rahul joined Akash.
Most Upvoted Answer
Akash started a business with Rs. 80,000 and after some months Rahul j...
Given:
- Akash started a business with Rs. 80,000.
- Rahul joined the business after some months with Rs. 75,000.
- The profit at the end was distributed in the ratio of 8:5.
To find:
- After how many months did Rahul join Akash?
Assumptions:
- Akash worked throughout the year, so his investment remained constant.
- The profit is distributed based on the ratio of their investments.
Solution:
Let's assume Rahul joined after 'x' months.
Initial Investments:
- Akash: Rs. 80,000
- Rahul: Rs. 0 (as he joined later)
Investments after 'x' months:
- Akash: Rs. 80,000
- Rahul: Rs. 75,000
Profit distribution:
The profit will be distributed in the ratio of their investments, which is 8:5.
Profit share of Akash:
Akash's profit share = (Akash's investment / Total investment) * Total profit
= (80,000 / (80,000 + 75,000)) * Total profit
= (80,000 / 155,000) * Total profit
Profit share of Rahul:
Rahul's profit share = (Rahul's investment / Total investment) * Total profit
= (75,000 / (80,000 + 75,000)) * Total profit
= (75,000 / 155,000) * Total profit
Given that the profit share ratio is 8:5, we can write the following equation:
(80,000 / 155,000) * Total profit / (75,000 / 155,000) * Total profit = 8/5
Simplifying the equation, we get:
80,000 / 75,000 = 8/5
Cross-multiplying, we get:
80,000 * 5 = 75,000 * 8
400,000 = 600,000
The equation is not satisfied, which means our assumption that Rahul joined after 'x' months is incorrect.
Assuming Rahul joined after 'x' months:
Let's assume Rahul joined after '4' months.
Investments after 4 months:
- Akash: Rs. 80,000
- Rahul: Rs. 75,000
Profit distribution:
The profit will be distributed in the ratio of their investments, which is 8:5.
Profit share of Akash:
Akash's profit share = (Akash's investment / Total investment) * Total profit
= (80,000 / (80,000 + 75,000)) * Total profit
= (80,000 / 155,000) * Total profit
Profit share of Rahul:
Rahul's profit share = (Rahul's investment / Total investment) * Total profit
= (75,000 / (80,000 + 75,000)) * Total profit
= (75,000 / 155,000) * Total profit
Given that the profit share ratio is 8:5
- Akash started a business with Rs. 80,000.
- Rahul joined the business after some months with Rs. 75,000.
- The profit at the end was distributed in the ratio of 8:5.
To find:
- After how many months did Rahul join Akash?
Assumptions:
- Akash worked throughout the year, so his investment remained constant.
- The profit is distributed based on the ratio of their investments.
Solution:
Let's assume Rahul joined after 'x' months.
Initial Investments:
- Akash: Rs. 80,000
- Rahul: Rs. 0 (as he joined later)
Investments after 'x' months:
- Akash: Rs. 80,000
- Rahul: Rs. 75,000
Profit distribution:
The profit will be distributed in the ratio of their investments, which is 8:5.
Profit share of Akash:
Akash's profit share = (Akash's investment / Total investment) * Total profit
= (80,000 / (80,000 + 75,000)) * Total profit
= (80,000 / 155,000) * Total profit
Profit share of Rahul:
Rahul's profit share = (Rahul's investment / Total investment) * Total profit
= (75,000 / (80,000 + 75,000)) * Total profit
= (75,000 / 155,000) * Total profit
Given that the profit share ratio is 8:5, we can write the following equation:
(80,000 / 155,000) * Total profit / (75,000 / 155,000) * Total profit = 8/5
Simplifying the equation, we get:
80,000 / 75,000 = 8/5
Cross-multiplying, we get:
80,000 * 5 = 75,000 * 8
400,000 = 600,000
The equation is not satisfied, which means our assumption that Rahul joined after 'x' months is incorrect.
Assuming Rahul joined after 'x' months:
Let's assume Rahul joined after '4' months.
Investments after 4 months:
- Akash: Rs. 80,000
- Rahul: Rs. 75,000
Profit distribution:
The profit will be distributed in the ratio of their investments, which is 8:5.
Profit share of Akash:
Akash's profit share = (Akash's investment / Total investment) * Total profit
= (80,000 / (80,000 + 75,000)) * Total profit
= (80,000 / 155,000) * Total profit
Profit share of Rahul:
Rahul's profit share = (Rahul's investment / Total investment) * Total profit
= (75,000 / (80,000 + 75,000)) * Total profit
= (75,000 / 155,000) * Total profit
Given that the profit share ratio is 8:5
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Akash started a business with Rs. 80,000 and after some months Rahul joined him with Rs. 75000. If the profit at the end was distributed in the ratio of 8 5, then after how many months did Rahul join Akash? (Assume Akash has worked throughout the year).a) 4b) 6c) 8d) 2Correct answer is option 'A'. Can you explain this answer?
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