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P and Q started a partnership business investing some amount in the ratio of 3:5. R joined them after six months with an amount equal to that of Q. In what proportion should the profit at the end of one year be distributed among P, Qand R?
- a)5 : 8 : 10
- b)6 : 10 : 5
- c)6 : 4 : 10
- d)10 : 6 : 3
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
P and Q started a partnership business investing some amount in the ra...
Let the initial investments of P and Q be 3a amd 5a.
P : Q : R = (3a x 12) : (5a x 12) : (5a x 6) = 36 : 60 : 30 = 6 : 10 : 5.
P : Q : R = (3a x 12) : (5a x 12) : (5a x 6) = 36 : 60 : 30 = 6 : 10 : 5.
Most Upvoted Answer
P and Q started a partnership business investing some amount in the ra...
Let the initial investments of P and Q be 3a amd 5a.
P : Q : R = (3a x 12) : (5a x 12) : (5a x 6) = 36 : 60 : 30 = 6 : 10 : 5.
P : Q : R = (3a x 12) : (5a x 12) : (5a x 6) = 36 : 60 : 30 = 6 : 10 : 5.
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P and Q started a partnership business investing some amount in the ra...
Given information:
- P and Q started a partnership business investing some amount in the ratio of 3:5.
- R joined them after six months with an amount equal to that of Q.
- The profit at the end of one year should be distributed among P, Q, and R in a certain proportion.
To find: The proportion in which the profit should be distributed among P, Q, and R.
Solution:
Let's assume that P invested 3x and Q invested 5x.
Therefore, the total investment by P and Q = 3x+5x = 8x.
R joined after six months with an amount equal to that of Q, which means R invested 5x as well.
Therefore, the total investment by P, Q, and R = 8x+5x = 13x.
Let's assume that the total profit earned by the business at the end of one year is Rs. y.
Now, we need to find the proportion in which the profit should be distributed among P, Q, and R.
- P's share in the profit:
P invested for the entire year, which is 12 months.
Therefore, P's share in the profit = (3x/13x) × y = (3/13) × y
- Q's share in the profit:
Q invested for the entire year, which is 12 months.
Therefore, Q's share in the profit = (5x/13x) × y = (5/13) × y
- R's share in the profit:
R invested for only 6 months.
Therefore, R's share in the profit = (5x/13x) × (6/12) × y = (5/26) × y
- Simplifying the above expressions:
P's share = (3/13) × y = (9/39) × y
Q's share = (5/13) × y = (15/39) × y
R's share = (5/26) × y = (10/39) × y
- Therefore, the proportion in which the profit should be distributed among P, Q, and R is:
9 : 15 : 10
Simplifying this ratio, we get:
3 : 5 : 2
Hence, the correct option is (B) 6:10:5.
- P and Q started a partnership business investing some amount in the ratio of 3:5.
- R joined them after six months with an amount equal to that of Q.
- The profit at the end of one year should be distributed among P, Q, and R in a certain proportion.
To find: The proportion in which the profit should be distributed among P, Q, and R.
Solution:
Let's assume that P invested 3x and Q invested 5x.
Therefore, the total investment by P and Q = 3x+5x = 8x.
R joined after six months with an amount equal to that of Q, which means R invested 5x as well.
Therefore, the total investment by P, Q, and R = 8x+5x = 13x.
Let's assume that the total profit earned by the business at the end of one year is Rs. y.
Now, we need to find the proportion in which the profit should be distributed among P, Q, and R.
- P's share in the profit:
P invested for the entire year, which is 12 months.
Therefore, P's share in the profit = (3x/13x) × y = (3/13) × y
- Q's share in the profit:
Q invested for the entire year, which is 12 months.
Therefore, Q's share in the profit = (5x/13x) × y = (5/13) × y
- R's share in the profit:
R invested for only 6 months.
Therefore, R's share in the profit = (5x/13x) × (6/12) × y = (5/26) × y
- Simplifying the above expressions:
P's share = (3/13) × y = (9/39) × y
Q's share = (5/13) × y = (15/39) × y
R's share = (5/26) × y = (10/39) × y
- Therefore, the proportion in which the profit should be distributed among P, Q, and R is:
9 : 15 : 10
Simplifying this ratio, we get:
3 : 5 : 2
Hence, the correct option is (B) 6:10:5.
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