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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 average becomes 17.5 then the number of natural numbers is –

A. 20 B. 30 C. 15 D. 10 Answer: Option D
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Solution(By Apex Team)

Let the number of natural numbers = n ∵ The average of some natural numbers = 15 ⇒ Sum of these natural number = 15 × n = 15n ∵ 30 is added and 5 is subtracted So, now addition of these number = 15n + 30 – 5 = 15n + 25 According to the question, $\begin{array}{l}\Rightarrow\left(\Large\frac{15n+25}{n}\right)=17.5\\ \Rightarrow15\mathrm{n}+25=17.5\mathrm{n}\\ \Rightarrow2.5\mathrm{n}=25\\ \Rightarrow\mathrm{n}=10\end{array}$ Therefore, The numbers of natural numbers n = 10

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