In a 100m race, A beats B by 20m. B beats C by 20m. What is the distan

Question

In a 100m race, A beats B by 20m. B beats C by 20m. What is the distance by which A beats C ?

A. 20
B. 36
C. 40
D. 50
E. cannot be determined

A beats B by 20 meters
A - 100
B - 80
A/B = 100/80

B beats C by 20 meters
Say in a 100-meter race, B -100
C - 80
B/C = 100/80

A/B*B/C = 100/80*100/80 = A/C = 100/64

So in a 100 meter race, A beats C by 36 meters.

B is the answer.

Vinit800HBS · Answer

B covers 80% of what A covers and C covers 80% of what B covers.

So, C will cover 80% of 80% Of distance that A covers I.e. 64%

Thus, C is lagging behind by (100-64)% of the race length.

Hence, C lags by 36meters

Posted from my mobile device

IP1992 · Answer

Distance ratio:
A:B=100:80=500:400

B:C=100:80=400:320

A Beats C in
500 m race by 180 meter
100 m race by (180*100/500)=36 meter.

Posted from my mobile device

GMATGuruNY · Answer

The prompt should state that the rates are constant

In a 100m race, A beats B by 20m. 
Since B is 20 meters behind A when A completes the 100-meter race, B travels 80 meters in the time it takes A to travel 100 meters:
 \frac{A}{B} = \frac{100}{80} = \frac{5}{4}

B beats C by 20m .
Since C is 20 meters behind B when B completes the 100-meter race, C travels 80 meters in the time it takes B to travel 100 meters:
 \frac{B}{C} = \frac{100}{80} = \frac{5}{4}

Thus:
 \frac{A}{C} = \frac{A}{B }* \frac{B}{C} = \frac{5}{4} * \frac{5}{4} = \frac{25}{16} = \frac{100}{64}

Since  \frac{A}{C} = \frac{100}{64} , C travels 64 meters in the time it takes A to complete the 100-meter race, with the result that A beats C by 36 meters.

B

samarpan.g28 · Answer

Hi. I could not see the question right below the timer. It was the solution provided by Chethan92 directly. Kindly help.

Bunuel · Answer

_______________________
Fixed the issue. Thank you!

findingmyself · Answer

Posting my solution here in case if someone might want to have a look.

When A travels 100M B travels 80M and they take the same time.
So we can write 100/Sa=80/Sb

Similarly we can write 100/Sb=80/Sc

From this we can find ratio of Sa: Sb: Sc
We will get Sa: Sb: Sc as 25:20:16
And we can derive Da:Db:Dc as the same ratio as Sa:Sb:Sc
Multiply equation by 4, we get 100:80:64 is Da:Db:Dc

So diff is Dc-Da=100-64=36

I might be completely wrong here, Wanted to hear from any of you if this apprach is correct

egmat · Answer

Hi findingmyself,

Good news: your approach is  completely valid , and it lands on the correct answer ( B ,  36 m). Let me confirm the one link that you seemed unsure about.

Why speed ratios give you distance ratios.

The whole method rests on one idea: in a race, everyone runs for the  same amount of time  until the winner finishes. When time is fixed, distance is directly proportional to speed (distance = speed x time). So if Sa : Sb : Sc =  25  :  20  :  16 , then the distances they cover in that same time are in the  exact same ratio . That is why you can jump straight from the speed ratio to Da : Db : Dc =  100  :  80  :  64 . This step is legitimate.

Your setup was right too:
-  100 /Sa =  80 /Sb gives Sa : Sb =  5  :  4  =  25  :  20 
-  100 /Sb =  80 /Sc gives Sb : Sc =  5  :  4  =  20  :  16 
- Chaining them: Sa : Sb : Sc =  25  :  20  :  16  ✓

Scaling so A runs the full  100 m, you get  100  :  80  :  64 , so A beats C by  100  -  64  =  36 m. This matches the ratio method GMATGuruNY posted (A/C =  5 / 4  x  5 / 4  =  25 / 16  =  100 / 64 ) - same result, just a different route.

One tiny label fix:  you wrote the difference as Dc - Da, but since A is ahead, it should be Da - Dc =  100  -  64  =  36 . The number is right; just flip the order so the gap comes out positive.

So trust this method - the key insight is simply that  equal time makes distance proportional to speed .

Answer: B

In a 100m race, A beats B by 20m. B beats C by 20m. What is the distan

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In a 100m race, A beats B by 20m. B beats C by 20m. What is the distan

Prep Toolkit

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