Question

The average weight of $40$ balls is $5$ grams. When the weight of the basket is added to the weight of balls, the average increased by $0.5$ grams. Find the weight of the basket.

Answer 1

Hint:
Here we are given the average weight of $40$ balls is $5$ grams. When the weight of the basket is added to the weight of balls, the average increased by $0.5$ grams. First find the total weight of $40$balls and after that average weight of $40$balls and a basket. After that, find the total weight of $40$balls and a basket and then Weight of basket$=$ The total weight of $40$balls and a basket$-$ total weight of $40$balls. Try it, you will get the answer,

Complete step by step solution:
We are given that the average weight of $40$ balls is $5$ grams. When the weight of the basket is added to the weight of balls, the average increased by $0.5$ grams.
So, total weight of $40$balls$=40\times 5=200$grams
So, as weight of basket and weight of ball are taken together,
Average weight of $40$balls and a basket$=5+0.5$ grams
Average weight of $40$balls and a basket$=5.5$ grams
Now the total weight of $40$balls and a basket$=5.5\times 41$grams
The total weight of $40$balls and a basket$=225.5$grams
Now we want to find the weight of basket,
Weight of basket$=$ The total weight of $40$balls and a basket$-$ total weight of $40$balls
We get,
Weight of basket$=225.5-200$grams
Simplifying we get,
Weight of basket$=25.5$grams

Therefore, the weight of the basket is $25.5$ grams.

Additional information:
Weighted average is an average in which each quantity to be averaged is assigned a weight. These weightings determine the relative importance of each quantity on average. Weightings are the equivalent of having that many like items with the same value involved in the average.

Note:
Weighted average is an average in which each quantity to be averaged is assigned a weight. These weightings determine the relative importance of each quantity on average. To find the weighted term, multiply each term by its weighting factor, which is the number of times each term occurs.