The following table shows the average speed (in km per hour) of five different trains A-E during six days of a week from Monday through Saturday. Some data is missing in the table ( indicated as '-') that you are expected to calculate, if required. Based on the data in the table, answer the question that follows: Train - wise speed (in km/hour) on different DaysTrain Average Speed (in km/hr) of Trains Monday Tuesday Wednesday Thursday Friday Saturday A 72 80 - 64 54 - B 88 - 80 84 72 90 C 54 70 72 - 64 60 D - 120 95 - 90 110 E 72 80 84 75 - -
For train A, if the average speed on Saturday is 20% more than that on Wednesday and the mean of the average speeds over all the six days is 67 km/hour then what is the average speed on Saturday?
72 km/hour
From the table, train A's known speeds are Monday 72, Tuesday 80, Thursday 64 and Friday 54. Only Wednesday and Saturday are missing.
Let Wednesday's speed = W. We are told Saturday is 20% more than Wednesday, so Saturday = 1.2W.
The mean over the six days is 67, so the total of all six days = 67 × 6 = 402.
Add the known days: 72 + 80 + 64 + 54 = 270.
Therefore W + 1.2W = 402 − 270 = 132, i.e. 2.2W = 132, so W = 60.
Saturday = 1.2 × 60 = 72 km/hour.
This is why 72 km/hour is correct. Values like 74 or 75 do not satisfy the mean-equals-67 condition once you solve for W.
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