The ages of 7 family members are 2, 5, 12, 18, 38, 40 and 60 years respectively. After 5 years a new member aged x years is added. If the mean age of the family now goes up by 1.5 years, then what is the value of x?

Explanation

Initial mean = \frac{175}{7} = 25. After 5 years, the mean of the 7 members naturally becomes 25 + 5 = 30, and their sum is 210. The new mean with the 8th member is 25 + 1.5 = 26.5. The new sum is 8 \times 26.5 = 212. Therefore, 210 + x = 212 \Rightarrow x = 2.

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