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. The λ is equal to?

Since mean is a linear operation, after taking product with the same number and subtracting the same number, the mean becomes 75λ - 25. We thus have by the condition given in the problem 75λ - 25 = 75 ⇒ λ = 43. So the correct answer is option B.