This problem involves calculating the rainfall for a specific year using average rainfall data over overlapping periods.

Calculating Total Rainfall for 2003-2005

The average rainfall for the three-year period 2003-2005 is given as 65 cm. The total rainfall for this period is calculated as:

Total Rainfall (2003-2005) = Average Rainfall $\times$ Number of Years

Total Rainfall (2003-2005) = $65 \text{ cm} \times 3 = 195 \text{ cm}$

Let $R_{2003}, R_{2004}, R_{2005}$ represent the rainfall in the years 2003, 2004, and 2005, respectively. So,

$R_{2003} + R_{2004} + R_{2005} = 195 \quad \text{(Equation 1)}$

Calculating Total Rainfall for 2002-2004

The average rainfall for the three-year period 2002-2004 is 63 cm. The total rainfall is:

Total Rainfall (2002-2004) = Average Rainfall $\times$ Number of Years

Total Rainfall (2002-2004) = $63 \text{ cm} \times 3 = 189 \text{ cm}$

Let $R_{2002}$ represent the rainfall in 2002. So,

$R_{2002} + R_{2003} + R_{2004} = 189 \quad \text{(Equation 2)}$

Determining 2002 Rainfall

We are given that the actual rainfall during 2005 was 60 cm. So, $R_{2005} = 60 \text{ cm}$.

Substitute the value of $R_{2005}$ into Equation 1:

$R_{2003} + R_{2004} + 60 = 195$

Subtracting 60 from both sides gives the combined rainfall for 2003 and 2004:

$R_{2003} + R_{2004} = 195 - 60$

$R_{2003} + R_{2004} = 135 \quad \text{(Equation 3)}$

Now, substitute the value of $(R_{2003} + R_{2004})$ from Equation 3 into Equation 2:

$R_{2002} + 135 = 189$

To find the rainfall in 2002, subtract 135 from both sides:

$R_{2002} = 189 - 135$

$R_{2002} = 54 \text{ cm}$

Therefore, the rainfall in 2002 was 54 cm.