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In a 1600 m race, A beats B by 80 m and ...

In a 1600 m race, A beats B by 80 m and C by 60 m. If they run at the same time then by what distance will C beat B in a 400 m race?

A

`5(15)/(77)m`

B

`5(20)/(76)m`

C

`15(5)/(77)m`

D

none of these

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze the information given about the race between A, B, and C. ### Step-by-Step Solution: 1. **Understanding the Race Distances**: - In a 1600 m race, A beats B by 80 m. This means when A finishes the race (1600 m), B has run only 1600 m - 80 m = 1520 m. - A also beats C by 60 m. This means when A finishes the race (1600 m), C has run only 1600 m - 60 m = 1540 m. 2. **Establishing the Ratios of Speeds**: - From the above, we can establish the distances covered by B and C when A finishes the race: - Distance covered by B = 1520 m - Distance covered by C = 1540 m - The ratio of the distances covered by A, B, and C when A finishes the race is: - A : B : C = 1600 : 1520 : 1540 3. **Simplifying the Ratios**: - We can simplify the ratios: - A : B : C = 1600 : 1520 : 1540 - Dividing each term by 80 gives us: - A : B : C = 20 : 19 : 19.25 4. **Finding the Relative Speeds**: - The speeds can be considered in terms of a common unit. Let’s denote the speed of A as 20 units, B as 19 units, and C as 19.25 units. 5. **Calculating the Time Taken for 400 m Race**: - The time taken by A to run 400 m: - Time = Distance / Speed = 400 / 20 = 20 seconds. - During this time, we can find out how far B and C run: - Distance covered by B in 20 seconds = Speed of B × Time = 19 × 20 = 380 m. - Distance covered by C in 20 seconds = Speed of C × Time = 19.25 × 20 = 385 m. 6. **Finding the Distance C Beats B**: - In a 400 m race, when A finishes, B has covered 380 m and C has covered 385 m. - Therefore, the distance by which C beats B = Distance B covered - Distance C covered = 400 m - 380 m = 20 m. ### Final Answer: C will beat B by 5 m in a 400 m race.
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ARIHANT SSC-TIME, SPEED AND DISTANCE-EXERCISE LEVEL 1
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  2. In a kilometre race, A can give B a start of 20 m and also in a half k...

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  3. In a 1600 m race, A beats B by 80 m and C by 60 m. If they run at the ...

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  6. A beats B by 100 m in a race of 1200 m and B beats C by 200 m in a rac...

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  7. In a 1000 m race Ameesha gives a headstart of 100 m to Bipasha and bea...

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  8. In a 1000 metres race Ravi gives Vinod a start of 40 m and beats him b...

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  9. In a race the man who came two place ahead of the last man finished on...

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  11. A gives both B and C a start of 60 m in a 1500 m race. However, while ...

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  12. In a 600 m race Prabhat has a start of 200 m and the ratio of speeds o...

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  15. In a day how many times the minute-hand and hour-hand make right angle...

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  16. In a day how many times the minute-hand and hour-hand are opposite to ...

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  17. The relative speed of minute-hand with respect to hour-hand is:

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  18. What do the hands of a clock coincide between 5 and 6?

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  19. What is the angle between hour-hand and minute-hand as 2 : 25 pm?

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