Question

In a partnership business, the monthly investment by three friends for the first six months is in the ratio 3: 4: 5. After six months, they had to increase their monthly investments by 10%, 15%, and 20%, respectively, of their 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 (in the same order) at the end of the year such that the share is proportional to their individual total investment over the year?

• A. 22 : 23 : 24
• B. 22 : 33 : 50
• C. 33 : 46 : 60
• D. 63 : 86 : 110

Hint:

When calculating total investments with percentage increases, break the process into parts: calculate the initial total investment, then calculate the new investments after the percentage increase, and finally sum the investments for the total period.

Answer 1

The Correct Option is D

The investment ratio for the first six months is given as 3 : 4 : 5. After six months, each partner increases their investment by 10%, 15%, and 20%, respectively. We need to calculate the total investment for each partner over the entire year and find the ratio of their shares in the total profit.
Step 1: Calculate the total investment for the first six months.
Let the initial investments for the three partners be \( 3x \), \( 4x \), and \( 5x \) for the first six months.

Step 2: Calculate the increased investment for the next six months.
The new investments are calculated as follows: - Partner 1: \( 3x \times 1.1 = 3.3x \)
- Partner 2: \( 4x \times 1.15 = 4.6x \)
- Partner 3: \( 5x \times 1.2 = 6x \)

Step 3: Calculate the total investment for the year.
- Partner 1: Total investment \( = 3x \times 6 + 3.3x \times 6 = 18x + 19.8x = 37.8x \)
- Partner 2: Total investment \( = 4x \times 6 + 4.6x \times 6 = 24x + 27.6x = 51.6x \)
- Partner 3: Total investment \( = 5x \times 6 + 6x \times 6 = 30x + 36x = 66x \)

Step 4: Find the ratio of the total investments.
The ratio of their total investments is \( 37.8x : 51.6x : 66x \). Simplifying the ratio, we get: \[ 37.8 : 51.6 : 66 = 63 : 86 : 110 \] Thus, the correct ratio of their shares in the total profit is \( 63 : 86 : 110 \).