Three partners A, B and C shared the profit in a business in the ratio 6:9:10 respectively. If A,B and C invested the money for 12 months, 7 months and 5 months respectively, then the ratio of their investment is:
7:18:28       b) 2:3:5             c) 6:10:5            d) 4:7:8

We are given that the profits of partners A, B, and C are shared in the ratio of \(6:9:10\) respectively, and their investment durations are 12 months, 7 months, and 5 months.

Let their investments be denoted as \(I_A\), \(I_B\), and \(I_C\).

The formula for profit is:
\[
\text{Profit} = \text{Investment} \times \text{Time}
\]

This means that:
\[
\frac{I_A \times 12}{I_B \times 7} = \frac{6}{9} \quad \text{and} \quad \frac{I_A \times 12}{I_C \times 5} = \frac{6}{10}
\]

We will now solve for the ratios of the investments:

1. From \(\frac{I_A \times 12}{I_B \times 7} = \frac{6}{9}\):
   \[
   \frac{I_A}{I_B} = \frac{6}{9} \times \frac{7}{12} = \frac{7}{18}
   \]
   So, \(\frac{I_A}{I_B} = \frac{7}{18}\).

2. From \(\frac{I_A \times 12}{I_C \times 5} = \frac{6}{10}\):
   \[
   \frac{I_A}{I_C} = \frac{6}{10} \times \frac{5}{12} = \frac{1}{4}
   \]
   So, \(\frac{I_A}{I_C} = \frac{1}{4}\).

Thus, the ratio of their investments \(I_A : I_B : I_C\) is \(7:18:28\).

Therefore, the correct answer is:

\[
\boxed{7:18:28}
\]

---

Would you like more details or have any questions? 

Here are 5 related questions to deepen your understanding:

1. How do you calculate the individual investments from profit and time?
2. What happens to the investment ratio if the duration of investment changes for one partner?
3. How does the profit-sharing ratio affect the overall calculation?
4. What if A, B, and C invested for different time periods but the profits remained the same?
5. How do you solve for individual investments if the total profit is given?

**Tip:** Always double-check the time durations when solving partnership problems, as they significantly affect the final investment ratio.

Three partners A, B, and C shared the profit in a business in the ratio 6:9:10 respectively. If A, B, and C invested the money for 12 months, 7 months, and 5 months respectively, then the ratio of their investment is:
7:18:28   b) 2:3:5   c) 6:10:5   d) 4:7:8

Explore how to calculate the investment ratio for partners A, B, and C who share profits in a ratio of 6:9:10 while investing for different time periods. This problem involves the formula Profit = Investment × Time and is suitable for students in Grades 10-12.

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