Aloukya and Manoghna run in a circular track and they take 180 seconds and 150 seconds respectively to complete one revolution. If they start together at 9 am from the same point then they will meet again for the first time at $a b : c d$ AM.
Find the value of $a + b + c + d$ ?

Open in App

Solution

The required time taken is the LCM of 180 and 150
$180 = 2^{2} \times 3^{2} \times 5^{1}; 150 = 2 \times 3 \times 5^{2}$
LCM = $2^{2} \times 3^{2} \times 5^{2} = 900$ sec = 15 minutes
They meet again for the first time at $09 : 15$ AM
$a = 0, b = 9, c = 1, d = 5$
$a + b + c + d = 0 + 9 + 1 + 5 = 15$

Suggest Corrections

Similar questions

Q. Amit, Sucheta and Neeti start running around a circular track and complete one round in 18 seconds, 24 seconds and 32 seconds respectively. In how many seconds will the three meet again at the starting point if they all have started running at the same time?

Q. Three persons begin to walk around a circular track. The first completes revolution in

15 \frac{1}{6}

seconds, the second in

16 \frac{1}{4}

seconds and the third in

18 \frac{2}{3}

seconds, respectively. After what time will they be together at the starting point again?

Q. A,

B

and

C

start to run around a circular stadium at the same time, in the same direction. A completes a round in

252

seconds,

B

308

seconds and

C

198

seconds, all staring at the same point. After what time will they meet again at the starting point?

Three athletes A, B, C are participating in a racing event. They start running together. A takes 30 seconds to complete one round on the track, B takes 40 seconds and C takes 45 seconds. What is the minimum number of seconds after which will they all be at the same place again?

Q. A toy train completes one round of a circular track in

120

seconds. Another one completes a round in

180

seconds. Both the trains start together from a station and run in opposite direction.After how many minutes will both the trains meet for the first time at the station from where they started?

Join BYJU'S Learning Program

Aloukya and Manoghna run in a circular track and they take 180 seconds and 150 seconds respectively to complete one revolution. If they start together at 9 am from the same point then they will meet again for the first time at ab:cd AM.Find the value of a+b+c+d?

The required time taken is the LCM of 180 and 150180=22×32×51;150=2×3×52LCM = 22×32×52=900 sec = 15 minutesThey meet again for the first time at 09:15 AMa=0,b=9,c=1,d=5a+b+c+d=0+9+1+5=15

Aloukya and Manoghna run in a circular track and they take 180 seconds and 150 seconds respectively to complete one revolution. If they start together at 9 am from the same point then they will meet again for the first time at $a b : c d$ AM.
Find the value of $a + b + c + d$ ?