Average age 4

The average age of 31 people in a group is 19. If one person is reduced to 18, the average age becomes 18. Find the age of the reducing person.

Correct answer:

x =  49

Step-by-step explanation:

$$\begin{gathered} n_1=31 \\ {m}_1=19 \\ {n}_2=n_1-1=31-1=30 \\ {m}_2=18 \\ {m}_1=\frac{m_2\cdot n_2+x}{n_1} \\ {m}_1\cdot n_1=m_2\cdot n_2+x \\ x=m_1\cdot n_1-m_2\cdot n_2=19\cdot 31-18\cdot 30=49 \end{gathered}$$

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