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The sum of five positive, consecutive integers is $115$ . Find the value of the smallest integer among these.

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21

24

23

25

answer is A.

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Detailed Solution

Given, the sum of five positive consecutive integers

= 115

.
Let the five consecutive integers be

x, x + 1, x + 2, x + 3, x + 4

.
According to given condition,

x + x + 1 + x + 2 + x + 3 + x + 4 = 115

\Rightarrow 5 x + 10 = 115

\Rightarrow 5 x = 115 - 10

\Rightarrow 5 x = 105

\Rightarrow x = \frac{105}{5} = 21

The smallest integer

= 21

.
Hence, the correct option is 1.

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