Two ants A and B start from a point P on a circle at the same time, wi

Question

Two ants A and B start from a point P on a circle at the same time, with A moving clock-wise and B moving anti-clockwise. They meet for the first time at 10:00 am when A has covered 60% of the track. If A returns to P at 10:12 am, then B returns to P at

A. 10:45 am
B. 10:40 am
C. 10:27 am
D. 10:25 am
E. 10:18 am

A. 10:45 am
B. 10:40 am
C. 10:27 am
D. 10:25 am
E. 10:18 am

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chetan2u · Answer

When A and B meet, A has covered 60%, so B has covered 40%, and their speeds are in ratio A:B=60:40=3:2..

Next A completes the remaining 40% in 1012-1000=12 minutes, while B has to cover 60% of the route..
B would cover 40% route in 3/2 more time => 12*3/2=18..
So B would cover 60% in 18*60/40=27.

Hence B reaches 27 minutes after the ants meet at 1000, so at 1000+27=1027

C

ArunSharma12 · Answer

ants.png A and B meet at point M at 10:00 AM A travels the rest of the distance \frac{2D}{5} in 12 minutes, as it is given that A returns to P at 10:12 AM. when A travels \frac{3D}{5} , B travels \frac{2D}{5} . when A travels \frac{2D}{5} , B will travel: \frac{2D*5*2D}{5*3D*5} = \frac{4D}{15} B travels \frac{4D}{15} in 12 minutes. B will travel \frac{3D}{5} in \frac{12*15*3D}{4D*5} = 27 minutes. So B will take 27 minutes from point M to reach point P. Ans: C

Kinshook · Answer

Given: Two ants A and B start from a point P on a circle at the same time, with A moving clock-wise and B moving anti-clockwise. They meet for the first time at 10:00 am when A has covered 60% of the track.

Asked: If A returns to P at 10:12 am, then B returns to P at

When A.& B meet at 1000 hrs,
A has covered 60% & B has covered remaining 40% of the track
vA : vB =60:40 =3:2

A takes 12 mins to cover remaining 40% of the track 
B will take 12*3/2 = 18 min to cover 40% of the track
B will take 18*60/40 = 27 mins to cover remaining 60% of the track

B will reach P at 1027 hrs

IMO C

minustark · Answer

Ratio of speed of A and B = 3: 2
To cover remaining 40% ant A took 12 minutes. So for the total distance ant A took 12/.4 = 30 minutes and ant B took 45 minutes.
They started their journey (30-12)= 18 minutes before 10 am or, 9.42 am. So ant B will reach to P = 9.42 + 45 = 9.87 or 10.27 am.
C is the answer

fireagablast · Answer

60% covered @10am, returns at 10:12am --> goes 40% in 12min
40 = r*1/5
r=200

60:40 --> ratio of person A to person B 
3:2

3/2 = 200/x
x=400/3

Person B needs to go 60%
60 = 400/3*t
t = 180/400 = 18/40 = 9/20 = 27/60 = 27min

10:00am + 27min = 10:27am
C

gurmukh · Answer

A covers 40 % of the distance is 12 minutes so will cover 60% of the distance in 18 minutes. Now B has to cover 60% of the distance and his speed is 2/3 of A's speed. 
Therefore time taken by B =18×3/2 = 27 minutes
Option C is the answer

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ScottTargetTestPrep · Answer

We see that ant A must cover 40% of the track in 12 minutes, which means it covers the entire track (or the circumference of the circle) in 12/0.4 = 30 minutes. This means both ants start moving from P at 10:12 am - 30 minutes = 9:42 am. Furthermore, we see that since it takes ant A 10:00 am - 9:42 am = 18 minutes to cover 60% of the track, it will take ant B the same (i.e., 18 minutes) to cover the remaining 40% of the track when they meet at 10:00 am. So it will take ant B 18/0.4 = 45 minutes to cover the entire track. Since ant B begins moving from P at 9:42 am, ant B will return to P at 9:42 am + 45 minutes = 10:27 am.

Answer: C

dhaundiyalmanan · Answer

Eq1- Speed of a / speed of b = 3/2

Speed of a = 40/12
Speed of b = 60/t

Put the values in eq1 and find t which comes out to be 27.

So time taken by B is 27 mins more after A and B meet at 10:00am
Hence 10:27 is the answer.

I tried solving by long method but then realized that placing speed in the ratios is more efficient and easy. Hope it helps.

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Fdambro294 · Answer

To make it easier let the distance of circle = 10

When they meet, A covers 60% of 10 or 6

B covers 4

(1st) when they meet, there is a constant travel time for both A and B. This means the Ratio of Distances covered will be directly proportional to the Ratio of Constant Speeds

Dist A : Dist B = 6 : 4 = 3 : 2

Speed A : Speed B = 3 : 2

(2nd) A travels another 4 distance to get back around to point P. How long will it take B to cover this 4 distance too? (but keep in mind that B still needs to cover 6 to get back to P)

Same Distance A and B covers is 4, thus:

Ratio of Speeds is inversely proportional to Ratio of Time traveled

Speed A : Speed B = 3x : 2x

Time for A to cover 4 : Time for B to cover 4 = 2x : 3x

It Takes A another 12 minute to cover this distance.

2x = 12 ——- x = 6

B will take 3x = 18 minutes to cover this distance of 4

(3rd)
Takes B ———-18 min———- to cover a distance of 4

Then how long will it take B to cover 6 distance?

T = (18 * 6) / 4 = 27 minutes

B will return to P at 10 : 27 AM

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btsaami · Answer

1. Time taken by A to cover 40% of D= 12 min so another 40% = 12min and remaining 20% =6 min so total Time = 30 min to cover entire D by A. or 18 min to cover 60% of the distance.
So, time taken by B to cover 60% of the distance, 3/2= tB/18 =tB = 27 min. Hence, 10:27am

2. Let A=3m/min B= 2m/min from the ratio a/b= 3/2
Distance travelled by B = 3*12 = 36 m = 40% of total circular Path, D = 36= 2/5*D
D= 90m
Now calculate the time taken for B to cover 60% of distance, 
60%of 90 = 54m, 54=2*t
t=27 min after 10 am. Hence, B

3. A/B= tB/12 to cover 40% of the distance.
tb for 40% D= 3/2*12=18 min

So, for 60% = 18 min + 9 min=27 min or

For B 40% of D/60%of D = 18/t = t=27 min

Two ants A and B start from a point P on a circle at the same time, wi

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Two ants A and B start from a point P on a circle at the same time, wi

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