JAMB 2025 Mathematics · Question 36

The average weight of 15 iron bars is 1000 kg. If the heaviest iron bar is removed, the average weight is…

Question

The average weight of 15 iron bars is 1000 kg. If the heaviest iron bar is removed, the average weight is reduced by 5 kg. Find the weight in kg of the heaviest iron bar.

A.1170kg
B.1270kg
C.1070kg
D.1370kg

Answer: C. 1070kg

Explanation written with AI and checked against the answer key

1. Analyze the question

We are given the average weight of 15 iron bars. When one bar (the heaviest) is removed, the number of bars decreases to 14, and the average weight decreases by 5 kg. We need to find the specific weight of that removed bar.

2. Explain the concept

The formula for the average is:

\text{Average} = \frac{\text{Sum of values}}{\text{Number of values}}

From this, we can derive:

\text{Sum of values} = \text{Average} \times \text{Number of values}

3. Show the solution

Step 1: Find the total weight of the 15 iron bars.

\text{Total weight} = 15 \times 1000 = 15,000 \text{ kg}

Step 2: Find the new average and the new number of bars.

New number of bars = $15 - 1 = 14$
New average = $1000 - 5 = 995 \text{ kg}$

Step 3: Find the total weight of the remaining 14 iron bars.

\text{New total weight} = 14 \times 995

14 \times 995 = 13,930 \text{ kg}

Step 4: Calculate the weight of the removed bar.

\text{Weight of heaviest bar} = (\text{Original total}) - (\text{New total})

\text{Weight} = 15,000 - 13,930 = 1,070 \text{ kg}

4. Identify the answer

Comparing our result to the given options: A. 1170kg B. 1270kg C. 1070kg D. 1370kg

The correct option is C.

5. Tip

When dealing with "average" problems, always calculate the Total Sum first. It is much easier to work with the totals than to try to manipulate the averages directly. Also, double-check your subtraction—a small error in the final step is the most common way students lose marks in JAMB Mathematics!

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