Question 55

The mean of the 5 smallest numbers from a group is 15 while the mean of all the numbers of the group taken together is 17. If the mean of the numbers leaving the smallest five out is 18.25, how many numbers were there in the group in all?

Solution

Let total numbers be x

sum of 5 smallest numbers = 5 x 15 = 75

sum of remaining numbers = 18.25(x - 5)

According to the question,

75 + 18.25(x - 5) = 17x (17 is the mean of all numbers)

75 + 18.25x - 91.25 = 17x

16.25 = 1.25x

x = 13

Hence, option A is the correct answer.

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