$\text{Y}$ starts a business with an investment of $\text{Rs. }8,000$. Four months later, $\text{Z}$ joins by investing $\text{Rs. }3,500$. They partner for an entire year. What is the ratio of $\text{Y}$ 's profit to $\text{Z}$ 's profit at the end of the year?

In a partnership business, profit shares are divided in proportion to the product of investment capital and investment duration ($\text{Profit Ratio}=\text{Investment}\times \text{Time}$).
* For $\text{Y}$:
* Investment = $\text{Rs. }8,000$
* Time duration = $12\text{months}$ (entire year)
* Investment product equivalent = $8000\times 12=96000$

* For $\text{Z}$:
* Investment = $\text{Rs. }3,500$
* Time duration = $12-4=8\text{months}$
* Investment product equivalent = $3500\times 8=28000$

Now compute the profit ratio of $\text{Y}$ to $\text{Z}$:

$$\text{Ratio}=\frac{96000}{28000}=\frac{96}{28}$$

Simplifying by dividing by $4$:

$$\text{Ratio}=\frac{24}{7}=24:7$$