Two boys on their bikes start a race around a triangular track ABC. Starting from the point A simult

M4maths Previous Puzzles

21 Aug 2014 bike race

Two boys on their bikes start a race around a triangular track ABC. Starting from the point A simultaneously, one of them traverse the track in clockwise sense A-> B -> C & the other in anticlockwise sense A-> C-> B with their respective constant speed. After 4 min from the start, they first meet at B and then continue the race. After what minimum time they meet first at B, will they again meet at B? Distance AB=500m, BC=400m, CA=300m

OPtion

1) 12 min
2) 16 min
3) 24 min
4) 30 min
5) 36 min
6) 42 min
7) 48 min
8) 64 min
9) 74 min
10) none of these

Solution

Speed of boy moving clockwise =500/4 m/min
Speed of boy moving anticlockwise =700/4 m/min
Let us suppose they they will meet again after t min of first meeting then according to given condition

700*t/4 - 500 *t/4 = 1200n where n is minimum possible integer

So 200*t/4 = 1200 n
=>t = 24 n
on putting t on 700*t/4 & 500*t/4

we get these two as 700*(24n)/4; 500*(24n)/4
= 4200n; 3000n

we should choose n in such a way that 4200n & 300n would be multiple of 1200 & this is possible only for n=2 (min value)

so t = 48 min;

Correct Option: 7 Best Solution (54)

suman kumar   10 years AGO

Speed of First person =500/4=125m/min

Speed of second person=700/4=175m/min

speed of first person:speed of second person=125:175
=5/7 i.e. they will meet at B if A completes 5 revolution or b completes 7 revolution beacuse time taken by both of them are same. So, required time =5*(1200/125)=48 min

Like? Yes (25) | No (7)  

SUNITEE GARIMA   10 years AGO

speed of C=700/4=175m/min
speed of B=500/4=125m/min
time taken by C to complete one round acroos the traingular field=4+(500/175)=48/7min
time taken by B to complete one revolution=4+(700/125)=48/5min
time when they will meet again =LCM of 48/5 and 48/7=48

Like? Yes (13) | No (4)  

sruthi   10 years AGO

as time is same so speed ratio is similar to distance ratio= 700:500= 7:5
so totally they will meet at 12 points before they reach at B (since,7+5=12)
so at 13 th time they will be meet at B
since after 4 min they start, therefore 12*4=48 min they will meet again

Like? Yes (8) | No (2)  

NAVEEN KUMAR   10 years AGO

both meet at B
distance travell by first and second boy is 500&700
speed of 1 boy=500/4=125m/s
speed of 2nd boy=700/4=175m/s
if both meet at b then next dist. travell byboth in multiple of 1200.
so,for first boy (1200*(X1))/125=I(integer)
=(48*X1)/5= min val of x1=5
total time taken by first boy=(1200*5)/125=48
second boy(1200(X2))/175=I2(integer)
similarly ,X2=7
tatal time taken=(1200*7)/175=48
so ,we can say that minimum time they meet first at B is 48min

Like? Yes (5) | No (1)  

PURIDI MOUNIKA   10 years AGO

let's say the time to meet at point B =t
two persons are P & Q.
suppose P travels through A->B->C
Q travels through A->C->B
they both meet At B in 4 mins
So the distance travelled by P in 4 min=500 m
the speed of P =500/4=125 m/min
the distance travelled by Q in 4 min=700 m
the speed of Q =700/4=175 m/min
then the time for meeting At B for both of them =t (say)
for P, t=1200*x/175
for Q, t=1200*y/125
->1200*x/175=1200*y/125
->x/y=7/5
then x=7,y=5
t=1200*x/175=1200*7/175=48
so time=48 mins

Like? Yes (5) | No (1)  

sabir ahmd   10 years AGO

A finished one round in (4/500)*1200=48/5 min
B finished one round in (4/700)*1200=48/7 min

they will meet together after 48 mins.

Like? Yes (3) | No   

RAKESH   10 years AGO

their speeds = 500/4 , 700/4 = 125,175 m/min
time taken to complete track = 1200/125 , 1200/175
lcm(1200/125 , 1200/175 ) = 1200/25 = 48 min

Like? Yes (3) | No (1)  

Md.Sultan Khichi   10 years AGO

First man covers 500m in 4 mins so his speed is 500/4=125m/m.
2nd person covers 700m to reach B in 4 mins so his speed is 700/4=175 m/m.
Acorting to the ques they have to meet at B again..so if they wants to meet at B they should have to cover 1200m..now we have to check when they reached B together.when their speed totally divide the distance of 1200m or 1200m's multiple together at the same tym..
First person=1200/125=9.6(not totally divide).
2400/125=19.2
3600/125=28.8
4800/125=38.4
6000/125=48.
After 48 mins first person agn come at B.
Now at this tym where is the 2nd person..
2nd person=48*175=7200.
7200 is multiple of 1200..so 2nd person is also at B.
Ans..48 mins..

Like? Yes (2) | No (1)  

suman kumar   10 years AGO

let two boy be x and y.
taking x rotating clockwise from a to b (500m in 4min.)
then y rotating anticlockwise from a-c- b (700m in 4min.).
starting from b if both have to meet next time at b
total triange length=1200.
taking revolving time for x=1200/(500/4)min
taking revolving time for y=1200/(700/4)min
after taking the ratio since both will not rotate equal=5:7.
since after 5 rotation of x and 7 of y they will meet together.
thus, time=5*1200/(500/4)
ans :-48 min

Like? Yes (1) | No   

Malisetti Mounika   10 years AGO

they will meet at B on 13th time so
after 12 meetings which is 12*4=48

Like? Yes (2) | No (1)  

Himanshu Garg   10 years AGO

They meet first at B so one travels 500m and another travels 700m so they are meeting again & again by the ratio of 5:7
So, we calculate the distance by adding 5 and evaluate when the again 5 comes in our series

Hence 0 5 10 3 8 1 6 11 4 9 2 7 12 5
1 2 3 4 5 6 7 8 9 10 11 12

Now, 12* 4= 48min

Like? Yes (1) | No   

Abhishek Jain   10 years AGO

Time taken by first boy for 500 m and by second boy for 700 m is same. And they meet every time they covers the above distance. So They will meet at point B again on 12th time. Which will take 4*12 mins = 48 mins.

Like? Yes (2) | No (1)  

HARDIP BHALANI   10 years AGO

This is similar to a circular motion except for its triangular with different dimensions ! so once we have reached B so lets designate this as our starting point because time has to be calculated from here !!

So LCM (1200/125 , 1200/175) = 48 min

Like? Yes (2) | No (1)  

Ajay Kumar Gupta   10 years AGO

As time is same, so speed ratio = dist ratio = 7 : 5
so they will meet each other at 12 distinct positions in the track... hence at B they will meet again the 13th time
meeting time = 4 min
so after 12 such meetings i.e 12 * 4 = 48 mins they will again meet at B

Like? Yes (1) | No   

anandhakumar   10 years AGO

In 48 min both are travelling in 8400,6000 respectively

8400 and 6000 are divide by 1200

Answer is option 7) 48 min

Like? Yes (2) | No (1)  

selvakumar   10 years AGO

In 48 min both are travelling in 8400,6000 respectively

8400 and 6000 are divide by 1200

Answer is option 7) 48 min

Like? Yes (2) | No (1)  

ANKUR ANAND   10 years AGO

700/4x=1200*7
=>x=48min
answer 7)

Like? Yes (1) | No   

abhishek   10 years AGO

52 min.

Like? Yes (1) | No   

ravi shah   10 years AGO

speed of 1st bike covering distance AB=500/4=125m/min
speed of 2nd bike covering distance ACB=700/4=175m/min
Relative speed=175-125=25
so,time after which they meet=(500+300+400)/25=48 min

Like? Yes (1) | No   

KAPIL   10 years AGO

Speed of biker who traverse in clockwise sense=125 m/min
Speed of biker who traverse in anticlockwise sense=175 m/min
Perimeter of triangle= 1200 m
LCM of 125 and 1200 = 6000
So, Ist biker will reach at B after 6000/125 = 48 min
Similarly LCM of 175 and1200 =8400
So 2nd biker will reach at B after 8400/175 = 48 min

Like? Yes (1) | No   

Kushagra Tiwari   10 years AGO

This is similar to a circular motion except for its triangular with diferent dimensions ! so once we have reached B so lets designate this as our starting point because time has to be calculated from here !!

So LCM (1200/125 , 1200/175) = 48min !

Like? Yes (2) | No (1)  

Swechchha Agarwal   10 years AGO

As time is same, so speed ratio = dist ratio = 7 : 5

so they will meet each other at 12 distinct positions in the track... hence at B they will meet again the 13th time

meeting time = 4 min

so after 12 such meetings i.e 12 * 4 = 48 mins they will again meet at B

Like? Yes (1) | No   

yatish kumar sharma   10 years AGO

time for

Like? Yes (1) | No   

abhishek   10 years AGO

speed of 1st boy(b1) = 500/4
speed of 2nd boy(b2)=700/4
time taken by b1 to complete the whole round distance i.e 1200m,from pt b =1200/500*4=48/5
time taken by b2 to complete the whole round distance i.e 1200m, from pt b=1200/700*4=48/7
now they will meet second time @ pt b in (L.C.M of 48/5,48/7)= 48 min

Like? Yes (2) | No (1)  

TUSHAR    10 years AGO

8400

Like? Yes (1) | No   

mukesh   10 years AGO

speed of a and b is 48/5 and 48/7
so they will meet after 48 min

Like? Yes (1) | No   

Suresh Kashyap   10 years AGO

let clockwise biker x1 and anticlockwise biker x2
x1 travel 500m in 4 min
x2 travel 700m in 4 min
now they are at point B
they start again
after 12 comlete round they meet again at point B
so after 12x4=48min later ther meet again at B

Like? Yes (1) | No   

lalit   10 years AGO

after every 4 minutes both boy meet at a point.
the next time when boy who reach point b from a in clockwise direction will be on spot b when he has covered 6000m distance.
time reqired to cover 6000meter is (6000/500)*4=48minute

Like? Yes (1) | No   

sudipta maji   10 years AGO

THE RATIO OF THE DISTANCE COVER BYTHE TWO BOY A->B->C : A->C->B =5:7 AND THEIR SPEED WILL BE 125M/mand 175M/m
so the time is1200*5/125=48min

Like? Yes (1) | No   

Pushpendra singh chundawat   10 years AGO

let x and y be the no of rounds to be completed by the boys respectively.
hence speed will be 125 and 175 metr/min
so x=5 and y=7
now
time taken by both boys to meet-(1200*5)/125=48min
or
(1200*7)/175=48 min

Like? Yes (1) | No   

chanda.ajaykishore babu   10 years AGO

to reach b the they has to travel 1200 km with speeds 125 &161.5 after 12 loops that is 48 min only the slower reach point B at that time only the faster one reach the point B

Like? Yes (1) | No   

sankalp yadav   10 years AGO

its question similar to hc verma relative velocity topic.

Like? Yes (1) | No   

shiv pujan   10 years AGO

time to cover =48 min

Like? Yes (1) | No   

Dikesh Kumar Gumansingh   10 years AGO

total distance=1200m
time for 500 m=4
12*4=48

Like? Yes (1) | No (1)  

KAUSHAL KUMAR   10 years AGO

after min 48min they will again meet at B

Like? Yes (1) | No (1)  

AMIT SINGH   10 years AGO

after 48 mint they will meet at B point again

Like? Yes (1) | No (1)  

arpit farkya   10 years AGO

Lcm of(48/5,48/7)=48

Like? Yes (1) | No (1)  

Rajat sadhu   10 years AGO

ans.-48min
let x and y moving clockwise and anti clockwise around the triangular track ABC ,
speed of x=500/4=125m/min
speed of y=700/4=175m/min
they again meet at B when x completes n rounds and y completes m round of the track,then
1200*n/125=1200*m/175 (1200 is total distance of the track)
n/m=5/7
hence x completes 5 rounds and y completes 7 rounds after which they meet at B
required time=5*1200/125=48min

Like? Yes (1) | No (1)  

S.SHAFI   10 years AGO

Check option Substitution..
For p1, 4min ---> 500m
48min--> 6000m
For p2 4min-->700m
48min -->8400m
Total distance --> 1200m

6000m, 8400m are divisible by 1200m ... so after 48min they will meet at B.

Like? Yes (2) | No (2)  

Ravi Bhalani   10 years AGO

This is similar to a circular motion except for its triangular with different dimensions ! so once we have reached B so lets designate this as our starting point because time has to be calculated from here !!

So LCM (1200/125 , 1200/175) = 48 min

Like? Yes (1) | No (1)  

Harshad    10 years AGO

This is similar to a circular motion except for its triangular with different dimensions ! so once we have reached B so lets designate this as our starting point because time has to be calculated from here !!

So LCM (1200/125 , 1200/175) = 48 min

Like? Yes (1) | No (1)  

Chiranjit Agarwal   10 years AGO

determine the hcf of the individual speed of the boys and divide it with the total length of the track will give you the time after which they will meet again at B

Like? Yes (1) | No (1)  

RAJEEV KUMAR   10 years AGO

LCM (1200/125 , 1200/175) = 48 min

Like? Yes (1) | No (1)  

kajol nigam   10 years AGO

v1=700/4=175
v2=500/4=125
lcm of 1200/175, 1200/125 = 48min

Like? Yes (1) | No (1)  

jagdish sharma   10 years AGO

respective speed of both bikers =50m/min
total dist. b/w BB=1200
time=1200/50=24
but in 24 min bikers r not meet at B
multiple of 24 is 48 is right ans.

Like? Yes (1) | No (1)  

Parshant garg   10 years AGO

ist 5 10 3 8 1 6 11 4 9 2 7 12 5
2nd 7 2 9 4 11 6 1 8 3 10 5 12 7
after 48 min...

Like? Yes (1) | No (1)  

Urvashi Jain   10 years AGO

according to the question both boy1 and boy 2 meet at 4 min so
we know that speed=distance /time
boy1 speed=500/4=125
boy 2 speed=700/4=175
they again meet so total distance=1200
time =1200/125=48/5
time=1200/175=48/7
take lcm and hcf of 48/7 and 48/5
lcm/hcf=48/1=48 min
option (7)

Like? Yes (1) | No (1)  

sudhakar   10 years AGO

In 48 min both are travelling in 8400,6000 respectively

8400 and 6000 are divide by 1200

Answer is option 7) 48 min

Like? Yes (2) | No (2)  

Abhishek Vishwakarma   10 years AGO

This is similar to a circular motion except for its triangular with diferent dimensions ! so once we have reached B so lets designate this as our starting point because time has to be calculated from here !!

So LCM (1200/125 , 1200/175) = 48min !

Like? Yes (1) | No (1)  

naina   10 years AGO

This is similar to a circular motion except
for its triangular with diferent dimensions !
so once we have reached B so lets
designate this as our starting point because
time has to be calculated from here !!
So LCM (1200/125 , 1200/175) = 48min !

Like? Yes (1) | No (1)  

Jasmita Parmar   10 years AGO

This is similar to a circular motion except for its triangular with different dimensions . so once we have reached B so lets designate this as our starting point because time has to be calculated from here

So LCM (1200/125 , 1200/175) = 48min

Like? Yes (1) | No (1)  

prem kumar   10 years AGO

1200 divide into 12 parts so every 4 mins their meet one part
so 12*4=48mins

Like? Yes (1) | No (1)  

gouthamdaneti   10 years AGO

one of the boy cover 500m in 4 min and other cover 700m
so we get each of there speed and ratio between there speed is 7:5;there fore there distance covered ratio is 7:5;
that is they meet at B after one of them cover 7*1200 divide this distance by the highest speed among them

Like? Yes (1) | No (1)  

krishna kanth   10 years AGO

speed of 1st is 125m/min
2nd person is 175m/min
time taken by first person to complete 1 cycle is 48/5
second person is 48/7
lcm of 48/5,48/7=48
ans is 48 min

Like? Yes (1) | No (2)