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Akbar Ali

· started a discussion

· 1 Months ago

Qn 54 (Question:88871.0)

Didn't get the alternative method for qn 54.. please explain..

Question:

The average of n consecutive integers is x and the average of the immediate next m consecutive integer is x + 8. Which of the following represents an appropriate relation between m and n?

Options:
A) m + n = 16
B) n – m = 16
C) \(\cfrac{m}{2}+\cfrac{n}{2}=16\)
D) \(\cfrac{n}{2}-\cfrac{m}{2}=16\)
Solution:
Ans: (a) If a is first term of the n consecutive integers, then

\(x=\cfrac{\frac{n}{2}(2a+n-1)}{n}=a+\cfrac{n}{2}-\cfrac{1}{2}\)......(i)

The next m consecutive integers will start with a + n.
So, x + 8 = \(x=\cfrac{\frac{m}{2}[2(a+n)+m-1]}{m}=a+n+\cfrac{m}{2}-\cfrac{1}{2}\) ......(ii)
Subtracting (i) from (ii), we get

\(8=\cfrac{n}{2}+\cfrac{m}{2}\Rightarrow m+n=16\)

Alternate method:


\(\cfrac{n}{2}+\cfrac{m}{2}=8\)

\(∴ n + m = 16\)

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