Question : The average of some natural numbers is 15. If 30 is added to the first number and 5 is subtracted from the last number, the new average becomes 17.5. What is the total number of natural numbers?
Option 1: 15
Option 2: 30
Option 3: 20
Option 4: 10
Correct Answer: 10
Solution :
Let the number of natural numbers = n
The sum of these natural numbers = 15 × n = 15n
Since 30 is added and 5 is subtracted.
15n + 30 – 5 = 15n + 25
According to the question,
$\frac{15n+25}{n}$ = 17.5
⇒ 15n + 25 = 17.5n
⇒ 2.5n = 25
$\therefore$ n = 10
Hence, the correct answer is 10.
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