Solution:

Using Kirchhoff's Laws, we can find the current through each resistance in the circuit.

Step 1: Draw the circuit diagram and label all the given values.

Step 2: Apply Kirchhoff's Voltage Law (KVL) to the circuit.

Starting from the positive terminal of the cell and moving in a clockwise direction, we have:

EMF = IR + I1R1 + I2R2

where E = 3V is the EMF of the cell, R = 4ohm is the internal resistance of the cell, I1 and I2 are the currents flowing through the two resistances, and R1 = 10ohm and R2 = 24ohm are the resistances of the two resistors.

Step 3: Apply Kirchhoff's Current Law (KCL) to the circuit.

At the junction where the two resistors are joined in parallel, the total current flowing into the junction is equal to the sum of the currents flowing through the two resistors.

Therefore, I1 = I2(R2 / (R1 + R2))

Step 4: Substitute the value of I1 in the KVL equation.

EMF = IR + I1R1 + I2R2

EMF = I(R + R1) + I2R2(R1 + R2) / (R1 + R2)

Step 5: Substitute the values of the given parameters in the equation and solve for I2.

3V = I(4ohm + 10ohm) + I2(24ohm)(10ohm + 24ohm) / (10ohm + 24ohm)

3V = 14I + 240I2 / 34

102V = 680I + 240I2

I2 = (102V - 680I) / 240

Step 6: Calculate the value of I1 using the formula derived in Step 3.

I1 = I2(R2 / (R1 + R2))

I1 = [(102V - 680I) / 240] x (24ohm / 34ohm)

I1 = (408V - 4080I) / 2850

Step 7: Substitute the value of I2 and I1 in the KVL equation to get the value of I.

EMF = IR + I1R1 + I2R2

3V = I(4ohm + 10ohm) + [(408V - 4080I) / 2850] x 10ohm + [(102V - 680I) / 240] x 24ohm

Solving this equation, we get:

I = 0.123A

Therefore, the current flowing through the 10ohm resistance is:

I1 = I2(R2 / (R1 + R2))

I1 = (0.123A) x (24ohm / 34ohm)

I1 = 0.087A

And the current flowing through the 24ohm resistance is:

I2 = (102V - 680I) / 240

I2 = (102V - 680 x 0.123A) / 240

I2 = 0.179A

Thus, the current flowing through the