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Rahul and Bharti are partners in a business. Rahul contributes 1/4th capital for 15 months and Bharti received 2/3 of profit. For how long Bharti money was used?
- a)8 months
- b)10 months
- c)11 months
- d)17 months
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Rahul and Bharti are partners in a business. Rahul contributes 1/4th c...
Understanding the Profit Sharing Scenario
In this partnership, we have two partners: Rahul and Bharti. The profit sharing is uneven, with Bharti receiving a larger portion (2/3 of the profit).
Initial Capital Contributions
- Rahul contributes 1/4 of the capital.
- Therefore, Bharti contributes the remaining capital:
- Bharti's contribution = Total Capital - Rahul's Contribution = 1 - 1/4 = 3/4 of the capital.
Duration of Capital Contribution
- Rahul's capital is used for 15 months.
- Let’s denote Bharti’s duration of capital use as \( x \) months.
Calculating Profit Shares
- The profit share is based on the product of capital and time.
- Rahul’s share of profit = \( \frac{1}{4} \times 15 = \frac{15}{4} \) capital-months.
- Bharti’s share of profit = \( \frac{3}{4} \times x \) capital-months.
Setting Up the Equation
Since Bharti received 2/3 of the total profit, we can equate their shares:
- Total profit = Rahul's share + Bharti's share
- Therefore, \( \frac{15}{4} + \frac{3}{4}x \).
Equating Bharti's share to 2/3 of the total profit:
Equation Formation
- \( \frac{3}{4}x = \frac{2}{3} \left( \frac{15}{4} + \frac{3}{4}x \right) \).
Solving for x
1. Multiply through by 12 to eliminate fractions:
\( 9x = 8 \left( \frac{15}{4} + \frac{3}{4}x \right) \)
\( 9x = 30 + 6x \)
2. Rearranging gives:
\( 3x = 30 \)
\( x = 10 \).
Conclusion
Thus, Bharti's money was used for 10 months, confirming option 'B' as the correct answer.
In this partnership, we have two partners: Rahul and Bharti. The profit sharing is uneven, with Bharti receiving a larger portion (2/3 of the profit).
Initial Capital Contributions
- Rahul contributes 1/4 of the capital.
- Therefore, Bharti contributes the remaining capital:
- Bharti's contribution = Total Capital - Rahul's Contribution = 1 - 1/4 = 3/4 of the capital.
Duration of Capital Contribution
- Rahul's capital is used for 15 months.
- Let’s denote Bharti’s duration of capital use as \( x \) months.
Calculating Profit Shares
- The profit share is based on the product of capital and time.
- Rahul’s share of profit = \( \frac{1}{4} \times 15 = \frac{15}{4} \) capital-months.
- Bharti’s share of profit = \( \frac{3}{4} \times x \) capital-months.
Setting Up the Equation
Since Bharti received 2/3 of the total profit, we can equate their shares:
- Total profit = Rahul's share + Bharti's share
- Therefore, \( \frac{15}{4} + \frac{3}{4}x \).
Equating Bharti's share to 2/3 of the total profit:
Equation Formation
- \( \frac{3}{4}x = \frac{2}{3} \left( \frac{15}{4} + \frac{3}{4}x \right) \).
Solving for x
1. Multiply through by 12 to eliminate fractions:
\( 9x = 8 \left( \frac{15}{4} + \frac{3}{4}x \right) \)
\( 9x = 30 + 6x \)
2. Rearranging gives:
\( 3x = 30 \)
\( x = 10 \).
Conclusion
Thus, Bharti's money was used for 10 months, confirming option 'B' as the correct answer.
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Community Answer
Rahul and Bharti are partners in a business. Rahul contributes 1/4th c...
Bharti’s share of profit = 2/3
Thus Rahul’s share of profit = 1 – 2/3 = 1/3
Hence profit sharing ratio of Rahul and Bharti = 1/3 : 2/3 = 1 : 3
Thus Rahul’s share of profit = 1 – 2/3 = 1/3
Hence profit sharing ratio of Rahul and Bharti = 1/3 : 2/3 = 1 : 3
Rahul’s share of capital = 1/4
So, Bharti’s share of capital = 1 – 1/4 = 3/4
So, Bharti’s share of capital = 1 – 1/4 = 3/4
Now let Bharti’s capital was used for y months
Therefore, one month equivalent capital of Rahul = 1/4 × 15 = 15/4
And one month equivalent capital of Bharti = 3/4 × y = 3y/4
Therefore, one month equivalent capital of Rahul = 1/4 × 15 = 15/4
And one month equivalent capital of Bharti = 3/4 × y = 3y/4
So, 15/4/3y/4 = 1/2
=> y = 10 (option ‘B’)
=> y = 10 (option ‘B’)
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Rahul and Bharti are partners in a business. Rahul contributes 1/4th capital for 15 months and Bharti received 2/3 of profit. For how long Bharti money was used?a)8 monthsb)10 monthsc)11 monthsd)17 monthsCorrect answer is option 'B'. Can you explain this answer?
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