Question 22

The mean of the 5 smallest numbers from a group is 21 while the mean of all the numbers of the group taken together is 25. If the mean of the numbers, leaving the smallest five out, is 27.5, how many numbers were there in the group in all?

Solution

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The mean of the 5 smallest numbers from a group is 21 while the mean of all the numbers of the group taken together is 25.The mean of the numbers, leaving the smallest five out, is 27.5.

Let the total numbers be $$(x+5)$$

According to the question,

$$\frac{21\times5 + 27.5\times x}{x+5}=25$$

$$105+27.5x = 25x +125$$

$$2.5x = 20$$

$$x = 8$$

Total numbers $$x+5 = 8+5 = 13$$

Option B is correct.

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