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 DShow Answer
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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