Two cars A and B start from diametrically opposite points of a circula

Question

Two cars A and B start at same time from diametrically opposite points of a circular track in opposite direction, with A moving clockwise and B moving anti-clockwise. If they meet each other for first time after A has traveled 20 miles, what is the length of circular track?

(1) The ratio of speed of A to B is 4:1.
(2) When A and B meet for the second time, B has traveled another 10 miles after meeting A for the first time.

New tricky question

chetan2u · Accepted Answer

Apart from the above method , a very logical and easy method would be " To work for the distance traveled as a part of total when they meet."

FIRST meeting -
when they both meet first, both have traveled HALF the length of track.
Let B travel x, and A travels 20, so half track = x+20
and total = 2(x+20)

lets see the statements-

(1) The ratio of speed of A to B is 4:1. 
When they meet for the first time,   both have traveled for SAME time.  
so if A travels 20 miles and the A:B speed ratio is 4:1, B will travel  \frac{20}{4}=5  miles.
so HALF track =  20+x=20+5=25 
full track =  2*25=50.. 
sufficient

(2) they meet again after B has traveled 10 miles. 
  This is TRICKY part  
How much have they traveled when they meet for second time? -  They travel a full track after the first meeting.. 
In this entire track, B travels 10 miles, so in half track he would cover  \frac{10}{2} = 5  miles..
so combined half track =  20+5=25.. 
full track =  2*25=50  miles
sufficient

D

niks18 · Answer

Let the speed of A & B be  u  &  v  respectively. To start with as they are moving towards each other from diametrically opposite points, hence when they will meet they would have covered half of the circumference.

=>πr=(u+v)*t , where  t  is the time take to meet

given  t=\frac{20}{u}

so  πr=(u+v)*\frac{20}{u} -------------------(1)

Hence length of circular track i.e. the circumference,  2πr=40+40\frac{v}{u}

Therefore we need the ratio of speeds of A & B to know the length

Statement 1:  directly provides the ratio.  Sufficient

Statement 2:  When they meet the second time, they would have traveled the complete circular path and time take is  \frac{10}{v}

so  2πr=(u+v)*\frac{10}{v} , divide this by equation (1) to get

2=\frac{10u}{20v}=>\frac{v}{u}=\frac{1}{4} . Hence we have the ratio of speeds.  Sufficient

Option  D

menonrit · Answer

Hi,

Could you please explain the second statement? How did you assume that B travelled 10 miles in this entire track.

Regards,

Ritvik

sonalchhajed2019 · Answer

Hi,
 Could you please explain the second statement? How did you assume that B travelled 10 miles in this entire track.

Could you please explain how can we know that he travelled 10 miles in the entire track ?

Regards,

apurv09 · Answer

Hi,
I'll try and explain.
since B has travelled only 10 miles while they meet again, means that A is faster than B. We have to find out the ratio of their speeds.
We take an easy assumption as 30 of the length of the track.
So, when A travels 20 B travels 10.
the ratio of their speed is 2:1
so when B travels another 10 miles A would travel 20 in the mean time and they meet gain

CrackverbalGMAT · Answer

This is a question based on relative speed concepts which in turn depends on the variation of distance with respect to speed, when time is kept constant.

When the time is constant, distance is directly proportional to speed. In other words, the ratio of distances travelled by two objects will be the same as the ratio of their speeds.

In the question, it’s given that A travelled 20 miles before A and B met each other for the first time. Let us evaluate the statements now.

Using statement I alone, we know the ratio of the speeds. Because both A & B started together and also ended up at the same point (when they met), we can say that they both travelled for the same time.

Because time is constant, the distances travelled by them will be in the same ratio of the speeds. So,

D_a  :  D_b  = 4:1.

But we know that  D_a  is 20. So, we will be able to find out  D_b . Hence, we will be able to find out one half of the length of the track – this is nothing but the sum of the distances travelled by A and B, right?

Therefore, we will be able to find out the length of the track uniquely (remember that, in DS, you don’t have to go for the exact answer all the time.). So, statement I alone is sufficient. Possible answer options are A or D. Options B, C and E can be eliminated.

Using statement II alone, we know that B has travelled a distance of 10 km by the time they meet for the second time. However, what will remain constant irrespective of the first or the second meeting is the ratio of their speeds. 
Let the length of the track be 2πr. Then, distance travelled by A, between the first meeting and the second meeting = 2πr – 10. Now,

\frac{(2πr – 10)}{10}  =  \frac{20}{(πr – 20)} .

Solving the above equation will definitely help us find a unique value of 2πr. Hence, statement II alone is also sufficient. Option A can be eliminated.

Correct answer option is D.

Although the second statement seems like it is not giving you much information, whatever information it is giving you is enough to solve the question, if you know the ratio concept highlighted throughout the solution.

Hope this helps!

Chandermohan · Answer

DexterZabula · Answer

Am I the only one who thought that "  they meet again after B has traveled 10 miles.  " meant that total distance traversed by B  from starting  is 10 miles?

chetan2u  : It's appreciable to frame question and help the community. But at the same time, it is imperative to construct the question in proper language. It may lead some students to doubt their concepts, robbing them crucial confidence and, consequently, some marks.

chetan2u · Answer

As far as statement II is concerned, even if someone takes 10 km as total distance traveled by B from beginning, it does not affect the answer. You should still get the statement as sufficient.

When A and B meet for the second time they have traveled 1.5 times the circle. 
As you have read the question, B travels 10 km. What about A?
A had travelled 20 km when they had covered 0.5 of circumference of circle within themselves, so A will cover 20*3 when 1.5 times the circumference of the circle is covered within themselves. 
Total distance traveled when they meet for the second time =10+60=70=1.5 times the route. 
So, the circle is of 70*2/3.

To help you further, I have changed the wording although it does not affect the question in any way.

DexterZabula · Answer

chetan2u  : Glad to see someone taking suggestion positively.

Now, if wordings had remained as they're, won't the answer be A?
On GMAT, two statements do NOT return different values of same variable!

chetan2u · Answer

Individual statement giving you a solution should get you to D. But, the question in actuals would never give you two different answers from the two statements. It will always be a unique solution.

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Two cars A and B start from diametrically opposite points of a circula

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