If N = $\frac{p}{2}$($\frac{T_1 - T_2}{T_1}$). Find P when N = 12, T1 = 27 and T2 = 24.

1. Analyze the question

We are given the formula $N = \frac{p}{2} \left( \frac{T_1 - T_2}{T_1} \right)$ and the values $N = 12$, $T_1 = 27$, and $T_2 = 24$. We need to isolate $p$ and calculate its value.

2. Explain the concept

This is a problem of substitution and algebraic manipulation. To solve for $p$, we need to rearrange the formula to make $p$ the subject of the equation. Once rearranged, we substitute the known values into the equation and simplify.

3. Show the solution

Step 1: Write down the formula

Step 2: Substitute the given values

Step 3: Simplify the fraction inside the bracket

Since $\frac{3}{27}$ simplifies to $\frac{1}{9}$:

Step 4: Solve for $p$ Multiply both sides by 18:

4. Identify the answer

Comparing our result to the given options: A. 48 B. 108 C. 54 D. 216

The calculated value matches option D.

5. Tip

When dealing with algebraic fractions in JAMB exams, always simplify the numbers inside the brackets first before performing cross-multiplication. This reduces the size of the numbers you are working with and minimizes the risk of calculation errors.