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Question 73
The average of six numbers $$N_1, N_2, N_3, N_4, N_5 and N_6$$ is A. 5 is subtracted from each number. What is the new average?
Solution
Given, $$\dfrac{N_1+N_2+N_3+N_4+N_5+N_6}{6} = A$$
=> $$N_1+N_2+N_3+N_4+N_5+N_6 = 6A$$ -- (1)
Then, $$\dfrac{N_1-5+N_2-5+N_3-5+N_4-5+N_5-5+N_6-5}{6} = \dfrac{N_1+N_2+N_3+N_4+N_5+N_6-30}{6}$$
Substituting (1),
$$\dfrac{6A-30}{6} = A-5$$
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