The mean of a set of 30 observations is 75. If each observation is multiplied by a non-zero number λ and then each of them is decreased by 25, their mean remains the same. Then λ is equal to :
A
13
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B
23
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C
43
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D
103
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Solution
The correct option is C43 Let the mean be, μ=75 ⇒30∑i=1xi30=75⋯(1)
Now, 30∑i=1(λxi−25)30=75 ⇒λ30∑i=1xi30−25=75
Using equation (1), λ×75−25=75⇒λ=43