A person borrowed $\text{₹}1760$ at $6\%$ per annum and $\text{₹}2240$ at $9\%$ per annum at simple interest for the same period. He had to pay $\text{₹}1536$ in all as interest. Find the time (in years).

Let the time period for which the money was borrowed be $T$ years.
The formula for Simple Interest ($\text{SI}$) is:

$$\text{SI}=\frac{P\times R\times T}{100}$$

Where:

* $P=\text{Principal amount}$
* $R=\text{Rate of interest per annum}$
* $T=\text{Time in years}$

According to the given condition, the total interest paid is the sum of the interests from both investments:

$$\text{Total SI}={\text{SI}}_1+{\text{SI}}_2=1536$$

Substitute the given values into the formula:

$$\left(\frac{1760\times 6\times T}{100}\right)+\left(\frac{2240\times 9\times T}{100}\right)=1536$$

Simplify each part:

$$\frac{10560T}{100}+\frac{20160T}{100}=1536$$

$$105.6T+201.6T=1536$$

Combine the like terms:

$$307.2T=1536$$

Solve for $T$:

$$T=\frac{1536}{307.2}$$

$$T=5$$

Therefore, the time period is $5$ years.