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?

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SSC CGL 2023 Tier-I Official Paper (Held On: 18 Jul 2023 Shift 3)
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  1. 160 m
  2. 140 m
  3. 150 m
  4. 200 m

Answer (Detailed Solution Below)

Option 3 : 150 m
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Detailed Solution

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Given:

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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