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In a partnership business the monthly investment by three friends for the first six months is m the ratio 3 :4 : 5. After six months, they had to increase their monthly investments by 10%, 15% and 20%, respectively, of then initial monthly investment. The new investment ratio was kept constant for the next six months.
What is the ratio of their shares in the total profit (m the same order) at the end of the year such that the share is proportional to their individual total investment over the year?
What is the ratio of their shares in the total profit (m the same order) at the end of the year such that the share is proportional to their individual total investment over the year?
- a)63 : 86 : 110
- b)33 : 46 : 60
- c)22 : 23 : 24
- d)22 : 33 : 50
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
In a partnership business the monthly investment by three friends for ...
Given, ratio of initial investment of friends P, Q, R is 3 : 4 : 5 respectively.
Ratio, after increment in investment of P, Q, R.
P increase the investment by 5%.
Q increase the investment by 10%
R increase the investment by 20%
i.e. 3 + (3 x 1.1) : 4 + (4 x 1.5) : 5 + (5 x 1.2)
= 6.3 : 8.6 : 11
= 63 : 86 : 110
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In a partnership business the monthly investment by three friends for ...
Given Information:
- Three friends invest in a partnership business.
- The monthly investment for the first six months is in the ratio 3:4:5.
- After six months, they increase their investments by 10%, 15%, and 20%, respectively.
- The new investment ratio is kept constant for the next six months.
To Find:
- The ratio of their shares in the total profit at the end of the year, proportional to their individual total investment over the year.
Assumptions:
- The profit is equally distributed among the partners.
- The investments are made at the beginning of each month.
Solution:
Step 1: Calculate the individual investments for the first six months.
Let the initial monthly investments be 3m, 4m, and 5m.
The total investment for the first six months is (3m + 4m + 5m) * 6 = 12m + 24m + 30m = 66m.
Step 2: Calculate the individual investments for the next six months.
The increased investments are 10% of 3m, 15% of 4m, and 20% of 5m.
So, the new monthly investments are (3m + 10% of 3m), (4m + 15% of 4m), and (5m + 20% of 5m).
Simplifying,
The new monthly investments are 3.3m, 4.6m, and 6m.
The total investment for the next six months is (3.3m + 4.6m + 6m) * 6 = 39.6m.
Step 3: Calculate the total investment for the year.
The total investment for the year is the sum of the investments for the first six months and the next six months.
Total investment = 66m + 39.6m = 105.6m.
Step 4: Calculate the ratio of shares in the total profit.
The ratio of shares is proportional to the individual total investment over the year.
The ratio of shares is (66m/105.6m) : (39.6m/105.6m) : (105.6m/105.6m).
Simplifying,
The ratio of shares is 63 : 38 : 110.
Step 5: Simplify the ratio to its simplest form.
Divide all the terms of the ratio by the greatest common divisor.
The simplified ratio is 63 : 38 : 110.
Further simplifying, the ratio is 33 : 19 : 55.
Step 6: Compare the simplified ratio with the given answer options.
The simplified ratio 33 : 19 : 55 matches with option A, which is 63 : 86 : 110.
Therefore, the correct answer is option A) 63 : 86 : 110.
- Three friends invest in a partnership business.
- The monthly investment for the first six months is in the ratio 3:4:5.
- After six months, they increase their investments by 10%, 15%, and 20%, respectively.
- The new investment ratio is kept constant for the next six months.
To Find:
- The ratio of their shares in the total profit at the end of the year, proportional to their individual total investment over the year.
Assumptions:
- The profit is equally distributed among the partners.
- The investments are made at the beginning of each month.
Solution:
Step 1: Calculate the individual investments for the first six months.
Let the initial monthly investments be 3m, 4m, and 5m.
The total investment for the first six months is (3m + 4m + 5m) * 6 = 12m + 24m + 30m = 66m.
Step 2: Calculate the individual investments for the next six months.
The increased investments are 10% of 3m, 15% of 4m, and 20% of 5m.
So, the new monthly investments are (3m + 10% of 3m), (4m + 15% of 4m), and (5m + 20% of 5m).
Simplifying,
The new monthly investments are 3.3m, 4.6m, and 6m.
The total investment for the next six months is (3.3m + 4.6m + 6m) * 6 = 39.6m.
Step 3: Calculate the total investment for the year.
The total investment for the year is the sum of the investments for the first six months and the next six months.
Total investment = 66m + 39.6m = 105.6m.
Step 4: Calculate the ratio of shares in the total profit.
The ratio of shares is proportional to the individual total investment over the year.
The ratio of shares is (66m/105.6m) : (39.6m/105.6m) : (105.6m/105.6m).
Simplifying,
The ratio of shares is 63 : 38 : 110.
Step 5: Simplify the ratio to its simplest form.
Divide all the terms of the ratio by the greatest common divisor.
The simplified ratio is 63 : 38 : 110.
Further simplifying, the ratio is 33 : 19 : 55.
Step 6: Compare the simplified ratio with the given answer options.
The simplified ratio 33 : 19 : 55 matches with option A, which is 63 : 86 : 110.
Therefore, the correct answer is option A) 63 : 86 : 110.
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In a partnership business the monthly investment by three friends for the first six months is m the ratio 3 :4 : 5. After six months, they had to increase their monthly investments by 10%, 15% and 20%, respectively, of then initial monthly investment. The new investment ratio was kept constant for the next six months.What is the ratio of their shares in the total profit (m the same order) at the end of the year such that the share is proportional to their individual total investment over the year?a)63 : 86 : 110b)33 : 46 : 60c)22 : 23 : 24d)22 : 33 : 50Correct answer is option 'A'. Can you explain this answer?
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