Question
Download Solution PDFIn a 1500 m race, X beats Y by 100 m and X beats Z by 240 m. By what distance does Y beat Z in the same race?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
In a 1500 m race, X beats Y by 100 m and X beats Z by 240
Calculation:
When x goes 1500 m , y goes 1500-100 = 1400 m
When x goes 1500 m , z goes 1500-240 = 1260 m
When y goes 1400 m , z goes 1260 m
When y goes 1500 m , z goes,
⇒ (1260/1400) × 1500m = 1350 m
Y beat Z in the same race by the distance of 1500 - 1350 = 150 m
Mistake Points The race should be calculated as 1500m when calculating Y beat Z in the same race
∴ The correct option is 3
Alternate Method
- When X finishes 1500 m, Y has run 1400 m.
- When X finishes 1500 m, Z has run 1260 m.
Now, we need to find the distance by which Y beats Z in the same race.
When Y finishes 1500 m, the ratio of the distances run by Y and Z is the same as when X finishes. This is because the ratio of their speeds remains constant.
So, the ratio of distances run by Y and Z when X finishes the race is:
We can simplify this ratio by dividing both terms by their greatest common divisor (GCD), which is 20:
This means when Y runs 70 units of distance, Z runs 63 units of distance.
When Y runs the entire 1500 m race, we can set up a proportion to find the distance Z runs:
Cross-multiplying gives:
So, when Y finishes the 1500 m race, Z has run 1350 m.
Therefore, Y beats Z by:
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