The following table shows the average speed (in km per hour) of five different…
2023
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 Days
Train | 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?
Answer: B. 72 km/hour — CONCEPTFor a set of six daily speeds, mean = total of the six speeds divided by 6. A percentage relation can express one missing speed in terms of the other…
- A.
70 km/hour
- B.
72 km/hour
- C.
74 km/hour
- D.
75 km/hour
Show answer & explanation
Correct answer: B
CONCEPT
For a set of six daily speeds, mean = total of the six speeds divided by 6. A percentage relation can express one missing speed in terms of the other before using the mean.
APPLICATION
Let Wednesday's speed be x km/hour. Then Saturday's speed is 20% more, so it is 1.2x km/hour.
The total speed for six days is 6 × 67 = 402 km/hour.
The known Monday, Tuesday, Thursday, and Friday values total 72 + 80 + 64 + 54 = 270 km/hour.
Therefore, x + 1.2x = 402 − 270 = 132, so 2.2x = 132 and x = 60.
Saturday's speed is 1.2 × 60 = 72 km/hour.
CROSS-CHECK
The six values 72, 80, 60, 64, 54, and 72 total 402, and 402 ÷ 6 = 67. Also, 72 is 20% more than 60, so both conditions are satisfied.
Result: Saturday’s average speed is 72 km/hour.