Q48. 48. The average of three numbers p, q and r is k. p is as much more than the average as q is less than the average. What is the value of r?
Detailed Solution
Given that the average of p, q, and r is k. So, (p + q + r) / 3 = k, which implies p + q + r = 3k. We are also given that p is as much more than the average (k) as q is less than the average (k).
Let this difference be 'x'. So, p = k + x And q = k - x Now substitute these values of p and q into the sum equation: (k + x) + (k - x) + r = 3k 2k + r = 3k Subtract 2k from both sides: r = 3k - 2k r = k Alternatively, if p is 'x' more than the average and q is 'x' less than the average, then the sum of p and q is (k+x) + (k-x) = 2k.
This means the average of p and q is (2k)/2 = k. If the average of p and q is k, and the average of p, q, and r is also k, then r must necessarily be k to maintain the overall average. This question is a straightforward application of the definition of average.
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