Q.What is the investment ratio of $A, B$ and $C$ if their profit ratio is 6:7:8 respectively and their investment time period ratio is 2:3:4 respectively?

Investment Ratio Calculation — A First Look

Imagine you and a friend decide to start a small business together. You put in ₹50,000, and your friend puts in ₹30,000. At the end of the year, you make a profit of ₹16,000. How should you split it?

The fair answer is not "half each" — you put in more money, so you should get a larger share. That's the entire intuition behind investment ratios: profit is shared in the same proportion as the money invested.

The Core Idea

An investment ratio is simply a comparison of the amounts different people (or groups) put into a venture. If you invest ₹50,000 and your friend invests ₹30,000, the ratio of your investment to theirs is:

Like any ratio, you simplify it by dividing both sides by their common factor (here, 10,000):

That's your investment ratio. It tells you that for every ₹5 you put in, your friend put in ₹3.

From Ratio to Profit Share

Now, how does this ratio translate into actual money? The total investment is ₹80,000. Your share of the total is:

Your friend's share is:

So the profit of ₹16,000 is split as:

• You: $\frac{5}{8} \times 16,000 = ₹10,000$
• Friend: $\frac{3}{8} \times 16,000 = ₹6,000$

Notice that $10,000 : 6,000$ simplifies to $5 : 3$ — the same as the investment ratio. Profit is always divided in the ratio of investment.

When Investments Are for Different Durations

Here's where it gets slightly more interesting. What if you invested ₹50,000 for the full year, but your friend invested ₹30,000 only for the last 6 months? Is it still fair to split profit 5:3?

No — because your money was at work for twice as long. The solution is to convert each investment into an equivalent "money × time" unit, called the product.

• Your product: $50,000 \times 12 = 6,00,000$ (rupee-months)
• Friend's product: $30,000 \times 6 = 1,80,000$ (rupee-months)

Now compare these products:

That's the effective investment ratio. Profit is now split in the ratio 10 : 3, not 5 : 3.

The Precise Statement …