A,B,C,D share profits in the ratio 6:5:12:3, B left the business for doing MBA, what is the new ratio between A,C,D 

When B leaves the business, the remaining partners A, C, and D will share the profits in the same ratio relative to their original shares.

The original ratio is \( 6:5:12:3 \) for A, B, C, and D, respectively.

When B leaves, we remove B's share from the ratio, leaving us with the ratio for A, C, and D, which is \( 6:12:3 \).

Now, to simplify this ratio:

1. The ratio \( 6:12:3 \) can be simplified by dividing each term by the greatest common divisor (GCD) of these numbers, which is 3.
2. Simplifying each term:

\[
\frac{6}{3} : \frac{12}{3} : \frac{3}{3} = 2 : 4 : 1
\]

So, the new ratio between A, C, and D is **2:4:1**.

Would you like more details or have any questions? Here are some related questions:

1. How would the ratio change if another partner left the business?
2. What happens if B rejoins the business after completing the MBA?
3. How can we calculate the total profit each partner would get?
4. What if the profits were initially split equally, how would the ratios look?
5. How do we determine the GCD of a set of numbers?

**Tip:** When simplifying ratios, always divide each term by the greatest common divisor to find the simplest form.

Explore how profit sharing ratios change when a partner leaves a business. Solve a specific problem where partners A, C, and D originally share profits in the ratio 6:5:12:3, and find out the new ratio after B leaves for MBA. Detailed step-by-step solution included.

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