If three staff of Myschool Limited agreed to share their salary arrears in the ration of their ages, which are…

Analysis

To solve this problem, we need to divide a total sum of money (N120,000) among three people based on a given ratio (18:20:22). We are specifically asked to find the share of the second person.

Concept: Ratio and Proportion

When a quantity is divided in a given ratio, the steps are:

1. Sum the ratio parts: Add all the numbers in the ratio together.
2. Find the fraction for the specific part: Place the specific person's ratio value over the total sum of the ratio.
3. Calculate the share: Multiply this fraction by the total amount of money.

Step-by-Step Solution

Step 1: Determine the total sum of the ratio. The ages are 18, 20, and 22. Total ratio = $18 + 20 + 22 = 60$

Step 2: Identify the ratio for the second staff. The second staff corresponds to the age 20. Ratio for the second staff = $20$

Step 3: Calculate the fraction of the total money for the second staff. Fraction = $\frac{\text{Second staff's ratio}}{\text{Total ratio}} = \frac{20}{60}$ Simplify the fraction: $\frac{20}{60} = \frac{1}{3}$

Step 4: Calculate the actual amount. Amount = $\text{Fraction} \times \text{Total Money}$ Amount = $\frac{1}{3} \times 120,000$ Amount = $40,000$

The second staff receives N40,000.

Conclusion

Comparing our result with the provided options: A. N36,000 B. N44,000 C. N40,000 D. N15,000

The correct option is C.

Exam Tip

When dealing with ratios, always simplify the ratio first if possible to make your calculations easier. In this case, the ratio 18:20:22 can be simplified to 9:10:11. If you add these (9+10+11 = 30), the calculation becomes $\frac{10}{30} \times 120,000$, which is $\frac{1}{3} \times 120,000 = 40,000$. Simplifying first often prevents errors with large numbers!