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 E, if the ratio of average speed on Saturday and Friday is 5:3, then the average speed on Saturday is ____% more than that on Friday.
Answer: A. \(66\frac{2}{3}\) — ConceptFor two positive quantities with ratio new:base = a:b, the percentage increase is ((a - b) / b) × 100%. Equivalently, a p% increase changes a base…
- A.
\(66\frac{2}{3}\)
- B.
\(33\frac{2}{3}\)
- C.
\(55\frac{2}{3}\)
- D.
\(77\frac{2}{3}\)
Attempted by 2 students.
Show answer & explanation
Correct answer: A
Concept
For two positive quantities with ratio new:base = a:b, the percentage increase is ((a - b) / b) × 100%.
Equivalently, a p% increase changes a base value B into B × (1 + p/100).
Application
From the ratio 5:3, let Friday speed be 3k and Saturday speed be 5k.
The increase is 5k - 3k = 2k.
Percentage increase = (increase / Friday speed) × 100 = (2k / 3k) × 100.
Therefore, percentage increase = (2/3) × 100 = 200/3% = \(66\frac{2}{3}\%\).
Cross-check
Take Friday speed as 60 and Saturday speed as 100. The increase is 40, so (40/60) × 100 = \(66\frac{2}{3}\%\), and 100:60 simplifies to 5:3.
The average speed on Saturday is \(66\frac{2}{3}\%\) more than that on Friday.