The mean of five numbers is 30. If one number is excluded, their mean becomes 28. The excluded number is :
a. 28
b. 30
c. 35
d. 38

Solution:

Consider x1, x2, x3, x4, x5 as the five numbers and one of the excluded number is x5

It is given that

Mean of five numbers = 30

We can write it as

(x1 + x2 + x3 + x4 + x5)/5 = 30

By cross multiplication

x1 + x2 + x3 + x4 + x5 = 150

x1 + x2 + x3 + x4 = 150 - x5

Divide both sides by 4

(x1 + x2 + x3 + x4)/4 = (150 - x5)/4 …. (1)

It is given that

Mean of four numbers = 28

(150 - x5)/4 = 28 from equation (1)

By cross multiplication

150 - x5 = 112

By further calculation

x5 = 150 - 112

x5 = 38

Therefore, the excluded number is 38.

✦ Try This: The mean of five numbers is 20. If one number is excluded, their mean becomes 18. The excluded number is :

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 14

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NCERT Exemplar Class 9 Maths Exercise 14.1 Problem 11

The mean of five numbers is 30. If one number is excluded, their mean becomes 28. The excluded number is : a. 28, b. 30, c. 35, d. 38

Summary:

The mean of five numbers is 30. If one number is excluded, their mean becomes 28. The excluded number is 38

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