Question : In 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?
Option 1: 160 m
Option 2: 140 m
Option 3: 150 m
Option 4: 200 m
Correct Answer: 150 m
Solution :
Given: The length of the race = 1500 m
And, X beats Y by 100 m
And X beats Z by 240 m.
When X is at 1500 m,
Y will be at 1500 – 100 = 1400 m
Z will be at 1500 – 240 = 1260 m
The ratio of distance covered by Y and Z = 1400 : 1260 = 10 : 9
$\therefore$ Distance by Y beats Z = $\frac{10-9}{10}×1500$ = 150 m
Hence, the correct answer is 150 m.
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