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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