**Calculation of Time Period of a Simple Pendulum**

The time period (T) of a simple pendulum is given by the formula:

T = 2π(l/g)^1/2

Where:
- T is the time period of the pendulum
- l is the total length of the pendulum
- g is the acceleration due to gravity on Earth (approximately 9.8 m/s^2)

**Calculating the Percentage Change in Time Period**

To calculate the percentage change in the time period, we need to determine the new time period (T') after the given changes in length and gravity. Let's consider the change in length as Δl and the change in gravity as Δg.

The new length of the pendulum can be calculated by increasing the original length (l) by 2 percent:

New length (l') = l + (2/100) * l = l + 0.02l = 1.02l

Similarly, the new gravity can be calculated by decreasing the original gravity (g) by 4 percent:

New gravity (g') = g - (4/100) * g = g - 0.04g = 0.96g

Now, we can substitute the new length (l') and new gravity (g') into the formula for the time period to calculate the new time period (T'):

T' = 2π(l'/g')^1/2
= 2π((1.02l)/(0.96g))^1/2

To determine the percentage change in the time period, we can use the following formula:

Percentage change = ((T' - T) / T) * 100

**Simplifying the Expression and Calculating the Percentage Change**

Let's simplify the expression for the new time period (T'):

T' = 2π((1.02l)/(0.96g))^1/2
= 2π(1.06l/g)^1/2
= 2π(1.06)^1/2 * (l/g)^1/2
= (1.06)^1/2 * T

Now, substitute this value of T' and the original value of T into the formula for the percentage change:

Percentage change = ((T' - T) / T) * 100
= (((1.06)^1/2 * T) - T) / T * 100
= ((1.06)^1/2 - 1) * 100

Using a calculator, we can determine the value of ((1.06)^1/2 - 1) and calculate the percentage change.

The final answer will be the percentage change in the time period of the simple pendulum if the length increases by 2 percent and the gravity decreases by 4 percent.

|∆T/T|*100 = (1/2)*|∆l/l|*100 + (1/2)*|∆g/g|*100
= (1/2)*2% + (1/2)*4%
= 3%