If the numbers M, N, Q are in the ratio 5:4:3, find the value of $\frac{2N - Q}{M}$

Analysis

To solve this problem, we need to use the properties of ratios. When quantities are given in a ratio, we can represent them as multiples of a common constant.

Concept

If $M:N:Q = 5:4:3$, we can assign a common multiplier, let's call it $x$, to each term:

• $M = 5x$
• $N = 4x$
• $Q = 3x$

By substituting these values into the given expression, the variable $x$ will cancel out, allowing us to find the numerical value of the expression.

Solution

Step 1: Substitute the values into the expression. The expression is:

Substitute $M = 5x$, $N = 4x$, and $Q = 3x$:

Step 2: Simplify the numerator.

So, the expression becomes:

Step 3: Perform the subtraction.

Now we have:

Step 4: Divide. Since $x$ is a common factor (and $x \neq 0$), they cancel out:

Conclusion

The value of the expression is 1. Comparing this to the given options: A. 2 B. 3 C. 1 D. 4

The correct option is C.

Exam Tip

Whenever you see a ratio problem where you are asked to find the value of a fraction involving those variables, you don't need to find the actual values of the numbers. Simply treat the ratio parts as the actual values (e.g., let $M=5, N=4, Q=3$). This saves time during your JAMB exam!