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 heav...

Answer Details

To solve this problem, we need to use what we know about averages and how they change when a value is removed from a set.

Step 1: Calculate the total weight of all 15 iron bars.
The average weight of 15 bars is \\(1000\\) kg.
This means the total weight of all the bars is: \[ \text{Total weight} = \text{Average} \times \text{Number of bars} = 1000 \times 15 = 15000 \text{ kg} \]

Step 2: Understand what happens when the heaviest bar is removed.
When the heaviest bar is removed, there are 14 bars left, and the average weight drops by 5 kg.
So, the new average is: \[ 1000 \text{ kg} - 5 \text{ kg} = 995 \text{ kg} \]

The total weight of the 14 remaining bars is: \[ \text{Total weight of 14 bars} = 995 \times 14 = 13930 \text{ kg} \]

Step 3: Find the weight of the heaviest iron bar.
The weight of the heaviest bar is the difference between the total weight of all bars and the total weight after it is removed: \[ \text{Weight of heaviest bar} = 15000 - 13930 = 1070 \text{ kg} \]

Key concept: Removing the heaviest bar lowers the average, and you can find the weight of the removed bar by computing the difference in totals.
So, the heaviest iron bar weighs 1070 kg.